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Tilted glazing: angle-dependence of direct solar heat gain and form-refining of complex facades

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Tilted glazing: angle-dependence of direct solar heat gain and form-refining of complex facades

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Content TILTED GLAZING: ANGLE-DEPENDENCE OF DIRECT SOLAR HEAT GAIN AND FORM-REFINING OF COMPLEX FACADES by Won Hee Ko A Thesis Presented to the FACULTY OF THE USC SCHOOL OF ARCHITECTURE UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree MASTER OF BUILDING SCIENCE May 2012 Copyright 2012 Won Hee Ko ii ACKNOWLEDGEMENTS This thesis was supported by a grant from Southern California Edison’s Design & Engineering Services (D&ES) group. It was developed as part of Southern California Edison’s Emerging Technology program under internal project number CWA -1 PO 4500302844. I would like to show my deep gratitude to Professor Marc Schiler. His guidance and support from the initial to the final level enabled me to develop an understanding of the subject. He has always encouraged me and broadened my perspectives on interesting aspects of research. This thesis would not have been possible without his keen insight and guidance. All of the time I spent with Marc gave me a great experience not only academically but also personally. He is the best mentor I have ever had in my life. Marc, it was a great honor for me to have you as my thesis chair. It is a pleasure to thank Professor Karen Kensek. Since I started my graduate studies at USC, she has always stimulated me to come up with new ideas, as well as introduced me to new technologies related to parametric design. She also gave me a great chance to participate in the research funding program of Southern California Edison. Karen, I am grateful in every possible way and hope to continue our collaboration in the future. I gratefully acknowledge Peter Simmonds for his advice and supervision, which gave this thesis a firm background. He inspired me to think and develop the research ideas with practical aspects of building industry. With his wide range of knowledge, he contributed to the success of this thesis. Peter, thank you for being one of my committee members and I hope we work together in the future. iii My special thanks goes to Nathan Miller, whose encouragement and supervision on parametric design and its application to research were some of the driving forces for this thesis. He taught me special parametric skills in the class that motivated me to develop a parametric algorithm, linking the precedent research to form-refinement process in this thesis. I am thankful to Greg Otto, who participated in the early stage of this research thesis. It was always great to discuss this thesis with him as he encouraged the development of new ideas. In his class, I utilized the knowledge from this research and applied it to façade system design. His deep understanding and guidance led to the successful development of my work. Greg, you have been and will always be an exceptional mentor to me. I hope to keep up our collaboration in the future. I owe my gratitude to Susie Kim, who is a staff member at GS E&C Corporation. As a representative of her company, she provided me sufficient data for one of the case study projects, International Finance Center. Thanks to her, I applied my research to the existing building project. I am indebted to my friends and my family for their inspiration and encouragement. Finally, I would like to express my appreciation to everyone who supported me in completing this thesis successfully. iv TABLE OF CONTENTS ACKNOWLEDGEMENTS ................................................................................................... ii LIST OF TABLES .............................................................................................................. vii LIST OF FIGURES ........................................................................................................... viii ABSTRACT ........................................................................................................................ xii Chapter 1 Introduction .................................................................................................. 1 1.1. Background .......................................................................................................... 2 1.2. Glazing Properties and Solar Heat Gain .............................................................. 3 1.3. Nature of Sunlight ................................................................................................ 5 1.4. ASHRAE 90.1 ....................................................................................................... 9 1.5. Goals and Objectives ...........................................................................................10 Chapter 2 Solar Heat Gain Coefficient Calculation .............................................. 13 2.1. Solar Radiation Incident on a Fenestration System ...........................................14 2.2. Determining Incident Solar Irradiation.............................................................. 15 2.3. Determining Solar Angle.....................................................................................16 2.4. Solar Optical Properties of Glazing .....................................................................19 2.5. Angular Dependence of Glazing Optical Properties .......................................... 20 2.6. Angular Dependent SHGC in Previous Research .............................................. 22 2.7. Detailed Optical Property Calculation ............................................................... 23 2.7.1. Optical Properties of Single Glazing layers................................................. 23 2.7.2. Uncoated Glass ........................................................................................... 24 2.7.3. Coated Glass................................................................................................ 25 2.8. Detailed SHGC Calculation ................................................................................ 26 Chapter 3 Direct Solar Heat Gain Calculation ...................................................... 32 3.1. Direct Solar Heat Gain Calculation .................................................................... 33 3.2. Spreadsheet for Direct Solar Heat Gain Calculation ......................................... 34 3.3. Simple Case Comparison in the Spreadsheet .................................................... 36 3.4. ASHRAE Baseline and Spreadsheet Calculation in Different Climates ............ 40 3.4.1. Prescriptive Building Envelope Option in ASHRAE .................................. 40 v 3.4.2. Spreadsheet Calculation Results in Four Climate Zones............................ 43 3.4.3. Direct Solar Heat Gain Analysis in Four Climate Zones............................. 47 Chapter 4 Case Studies ............................................................................................... 60 4.1. Tilted Glazing in Contemporary Building Projects .............................................61 4.2. Ropemaker Place, London, UK ...........................................................................61 4.2.1. Building Information .................................................................................. 62 4.2.2. Flat Façade and Tilted Façade Comparison based on the Spreadsheet ..... 64 4.3. Tencent Seafront Headquarters in Shenzhen, China......................................... 67 4.4. International Finance Center, Seoul, South Korea ............................................ 70 4.4.1. Building Information ................................................................................... 71 4.4.2. Flat Façade and Tilted Façade Comparison based on the Spreadsheet ......73 Chapter 5 Building Energy Simulation Programs ............................................... 76 5.1. Ecotect .................................................................................................................77 5.2. eQUEST .............................................................................................................. 80 5.3. IES/VE ............................................................................................................... 83 5.4. EnergyPro........................................................................................................... 86 5.5. Integration between Energy Calculation and Schematic Design Phase ............ 88 Chapter 6 Form-Refinement Process based on a Parametric Tool ................. 89 6.1. Introduction ....................................................................................................... 90 6.2. Galapagos; Genetic Algorithm in Grasshopper ................................................. 93 6.3. Conceptual Idea.................................................................................................. 95 6.4. Design Tool Documentation .............................................................................. 97 6.4.1. Base Tower Outline ..................................................................................... 99 6.4.2. Faceted Surfaces Construction ................................................................. 100 6.4.3. Surface Azimuth and Tilt Angle Extraction .............................................. 102 6.4.4. Linking the Master Spreadsheet to Grasshopper ..................................... 102 6.4.5. Galapagos; Form-Refining Process .......................................................... 104 6.5. Result and Observation .................................................................................... 104 Chapter 7 Conclusion ................................................................................................ 106 7.1. Summary and Conclusion .................................................................................107 7.2. Future Study..................................................................................................... 109 vi BIBLIOGRAPHY .............................................................................................................. 113 APPENDIX: Galapagos .................................................................................................... 115 vii LIST OF TABLES Table 1: Equation of time values for 2011 .........................................................................16 Table 2: Solar declination for 2011 ................................................................................... 17 Table 3: Building Envelope Requirement for Climate Zone2........................................... 40 Table 4: Building Envelope Requirement for Climate Zone3............................................41 Table 5: Building Envelope Requirement for Climate Zone5 and 6 ..................................41 viii LIST OF FIGURES Figure 1.1 and 1.2: The Seattle Central Library and International Finance Center ........................3 Figure 2: Variables used in the Fresnel equations ......................................................................7 Figure 3: Fresnel equations .....................................................................................................7 Figure 4: Brewster's angle ...................................................................................................... 8 Figure 5 and Equation 6: Solar radiation incident on a fenestration and SHGC Calculation ........ 14 Figure 6: Solar angles for vertical and horizontal surfaces ........................................................ 18 Figure 7: Variations with incident angle of solar-optical properties........................................... 21 Figure 8: Optical properties of a single glazing layer ................................................................23 Figure 9: Two band model in spectral data library 1 and library2..............................................26 Figure 10: Cosine law and surface incidence ...........................................................................34 Figure 11: Master spreadsheet................................................................................................ 35 Figure 12: Spreadsheet results, South Façade, Phoenix, AZ ......................................................36 Figure 13: Two different shaped-buildings in Rhino and Grasshopper ......................................36 Figure 14: South facades........................................................................................................ 37 Figure 15: West facades .........................................................................................................38 Figure 16: North facades........................................................................................................38 Figure 17: East facades ..........................................................................................................38 Figure 18: DSHG comparison: vertical glazing and 15 degree tilted glazing ...............................39 Figure 19: Low-e double glazing sy stem angular properties in Windows6 (SHGC(0°) = 0.248)...42 Figure 20: Low-e double glazing system angular properties in Windows6 (SHGC(0°) = 0.399) ..43 Figure 21: Tilt angle definition diagram ..................................................................................43 Figure 22: Spreadsheet result, Phoenix, Arizona .....................................................................44 Figure 23: Spreadsheet result, Miami, Florida.........................................................................45 Figure 24: Spreadsheet result, Minneapolis, Minnesota ...........................................................45 Figure 25: Spreadsheet result, New York City , New York .........................................................46 ix Figure 26: Total direct solar heat gain of glazing in different angle of tilt, Phoenix, AZ ...............48 Figure 27: Winter peak - summer peak, Phoenix, Arizona ........................................................49 Figure 28: Summer DSHG peak, Phoenix, AZ .........................................................................50 Figure 29: Total direct solar heat gain of glazing in different angle of tilt, Miami, FL ................. 51 Figure 30: Winter peak - summer peak, Miami, FL ................................................................. 52 Figure 31: Summer DSHG peak, Miami, FL ............................................................................ 52 Figure 32: Total direct solar heat gain of glazing in different angle of tilt in Minneapolis, MN .... 53 Figure 33: Winter peak - summer peak, Minneapolis, MN .......................................................54 Figure 34: Summer DSHG Peak, Minneapolis, MN ................................................................. 55 Figure 35: Total direct solar heat gain of glazing in different angle of tilt, New York City , NY......56 Figure 36: Winter Peak- summer Peak, New York City , NY ...................................................... 57 Figure 37: Summer DSHG Peak in New York City , NY ............................................................. 57 Figure 38: West façade, Ropemaker Place ..............................................................................62 Figure 39: Conceptual idea of tilted glazing, Ropemaker Place .................................................63 Figure 40: Adjacent details, Ropemaker Place.........................................................................64 Figure 41: Rhino 3d model with tilted surfaces........................................................................65 Figure 42: Rhino 3d model with spreadsheet calculation: vertical glazing and tilted glazing .......66 Figure 43: DSHG Comparison: vertical glazing and tilted glazing .............................................66 Figure 44: Tencent Seafront Headquarters: perspective and tilted glazing ................................ 67 Figure 45: Tilted glazing as shading device ............................................................................ 68 Figure 46: Optimal angle studies............................................................................................69 Figure 47: International Finance Center (IFC): under construction ..........................................70 Figure 48: IFC Plan: Ground floor and the second floor ........................................................... 71 Figure 49 IFC Elevation: Ground floor and the second floor..................................................... 71 Figure 50: Glazing properties ................................................................................................ 72 Figure 51: Glazing properties ................................................................................................. 72 Figure 52: Rhino 3D model with tilted surfaces ....................................................................... 73 x Figure 53: Rhino 3D model with spreadsheet calculation: vertical glazing and tilted glazing....... 74 Figure 54: DSHG Comparison: vertical glazing and tilted glazing ............................................. 74 Figure 55: Modeling tilted glazing in Ecotect........................................................................... 79 Figure 56: Modeling a complex façade in Ecotect .................................................................... 79 Figure 57: Tilt angle definition diagram .................................................................................. 81 Figure 58: Solar gain in vertical glazing ..................................................................................82 Figure 59: Solar gain in 15 degree inward tilt glazing ...............................................................82 Figure 60: Solar gain in 15 degree outward tilt glazing .............................................................82 Figure 61: Glazing properties in IES-VE .................................................................................84 Figure 62: Solar gain in vertical glazing ..................................................................................85 Figure 63: Solar gain in 15 degree inward tilt glazing ...............................................................85 Figure 64: Solar gain in 15 degree outward tilt glazing ............................................................ 86 Figure 65: Modeling tilted glazing in Energy Pro......................................................................87 Figure 66: A case project; a faceted building design .................................................................92 Figure 67: Galapagos, an evolutionary component in Grasshopper ...........................................94 Figure 68: Single-Objective: Galapagos ..................................................................................95 Figure 69: Multi-Objective: Galapagos ...................................................................................95 Figure 70: Grasshopper linked to spreadsheet.........................................................................96 Figure 71: Grasshopper definition structure ............................................................................ 97 Figure 72: Geometry construction process ............................................................................. 98 Figure 73: Sliders in Grasshopper and consequence geometry change ..................................... 98 Figure 74: Grasshopper definition: base tower outline .............................................................99 Figure 75: Base tower outline in Rhino ................................................................................. 100 Figure 76: Grasshopper definition: vertices of each surface .................................................... 101 Figure 77: Grasshopper definition: surface construction ........................................................ 101 Figure 78: Grasshopper definition: surface-angle information extraction ................................ 102 Figure 79: Master spreadsheet input cell location .................................................................. 103 xi Figure 80: Grasshopper definition: excel write and read ........................................................ 103 Figure 81: Grasshopper definition: Galapagos ....................................................................... 104 Figure 82: Resulted geometries............................................................................................ 105 Figure 83: Overall concept of building balance point ............................................................. 110 Figure 85: Conceptual sketches: a unitized façade system with tilted glazing ............................ 111 Figure 86: Master Spreadsheet …………………………………………………………..… …...Supplemental Files Figure 87: Grasshopper Definition ……………………………………….…………..………..Supplemental Files xii ABSTRACT Contemporary cities are in a transition phase from primarily planar surfaces to a more dynamic urban fabric. One of the main contributors to this change is the development of shaped high-rise buildings that are in strong contrast to box-shapes of the past. This tendency makes accurate building energy simulation more difficult. Although sophisticated software exists to predict the performance of buildings and help architects and engineers make better decisions that reduce energy use, such programs are generally not able to deal with complexities of unconventional façade design. This is especially critical in regard to fenestration of high-rise office buildings, which have a large proportion of glazed area. Therefore, it has become important to improve the ability of energy software to deal with more complex façade designs. This research thesis focused on the effect of angular dependence on direct solar heat gain (DSHG) from tilted glazing. Variables that affect the optical properties of inclined glazing have been researched. One of the main variables, angle of incidence was chosen to be investigated in this research. The prescriptive path in ASHRAE 90.1 (ASHRAE STANDARD: Energy Standard for Buildings Except Low-Rise Residential Buildings) defines requirements of glazing properties depending on climate and building type regardless of the angular dependence of DSHG. For example, current SHGC is independent of angle of incidence. This can lead to errors in the building performance prediction. To improve DSHG calculation, a master spreadsheet that includes incident angle calculation based on the specific location, time and surface azimuth was developed. The effect of incident angle was reflected in DSHG calculation based on perpendicular direct incident solar radiation and the effective SHGC to produce the spreadsheet. Using xiii this spreadsheet, one can predict the amount of DSHG through each area of tilted glazing, with time-dependence throughout the year. Next, an algorithm was developed in Grasshopper (a plug-in for Rhino 3D), linking to the master spreadsheet. This algorithm can extract the surface azimuth and tilt angle of any surface from a given faceted form of building in Rhino, and the surface information is input back into the spreadsheet to calculate the DSHG of the surface. Based on this process, one can easily see the total DSHG of a whole building. By using the algorithm, the DSHG values of a simple box-shaped building and a building with tilted geometry were obtained. The difference between the DSHG values clearly shows the importance of accounting for the angular dependence of glazing, which is not generally included in building simulation programs, energy codes, and even architects’ perceptions. Without visual editing software such as Grasshopper, this process would have been possible only with time-consuming calculations and multiple iterations in the past. At the present time, technical innovation allows such studies to be conducted in an easy, quick and accurate way. This algorithm was developed further in Grasshopper to demonstrate form refinement of faceted building facades with an emphasis on the angle-dependent DSHG of glazing, a key factor for determining cooling and heating load. The intent is to provide a visual tool where architects could fine tune their initial ideas for the massing of a building and help them determine a better angle of glazing for the building and its overall geometry in a specific climate zone. Hypothesis: Static and Parametric studies in angular dependence of direct solar heat gain will determine the locally optimal angle of the glazing for buildings with consideration to time-dependence. 1 Chapter 1 Introduction This research project focuses on the effect of angular dependence on Direct Solar Heat Gain (DSHG) in buildings with tilted glazing. In this chapter, optics and glazing properties are discussed, the research argument with regards to the ASHRAE Standard is explored, and the objectives of the study are presented, along with insights into the methodology and intended deliverable of this project. 2 1.1. Background Buildings account for 72% of electricity consumption and 39% of energy use in the United States (McLaren 2009). Therefore, the U.S. Green Building Council, the people who develop and manage Leadership in Energy and Environmental Design (LEED) Green Building Rating Systems, speculate that high performance buildings can reduce energy use by 24 - 50% with sustainable design and maintenance strategies (McLaren 2009). Many new buildings now pursue LEED certification. One of the credits under Energy and Atmosphere in LEED deals with energy modeling to enhance the early stages of the design process by providing a preview of life-cycle performance. Although sophisticated software exists to predict the performance of buildings, such programs are not always useful in helping architects make better decisions that reduce energy use, especially for complex shapes. Existing building simulation programs may not have either capability or user-friendliness to help architects make better decisions early in the design process that could reduce energy use. This is especially true with faceted and curvilinear building facades where the glazing is not necessarily vertical. Building codes and software often cannot handle these more unusual curtain wall constructions and dynamic geometries. Therefore, more detailed considerations of building performance criteria are needed, such as building enclosure properties, with regard to energy efficiency. Contemporary high-rise buildings can have complex configurations that are in strong contrast to the box-shaped buildings of the past (Figure 1.1, Figure 1.2). As these new buildings are also designed to have a high percentage of glazing area, the thermal characteristics of the buildings that come from facades have become much more 3 important than the typical, vertically glazed buildings that might have a smaller window to wall ratio. Figure 1.1 and 1.2: The Seattle Central Library, Official Website < http://www.spl.org/locations/central-library>, 2004 and International Finance Center, Seoul, WHK, 2011 1.2. Glazing Properties and Solar Heat Gain Three basic values are considered as main properties of glazing: the U-value, the Solar Heat Gain (SHGC), and the Visual Light Transmittance (VLT). The U-value refers to how well a building element conducts heat, the SHGC represents how well a building element transmits solar energy, and the VLT stands for the amount of visible light that passes through a glazing system, and is expressed as a percent (ASHRAE, 2005). All of these values are influenced by the incident angle of solar energy, but the effect of angular dependence on U-value is smaller than that of SHGC or VLT. This is because the U-value is mainly impacted by heat transfer per unit area and temperature difference between two sides. Only the convection rate change on the surface of a building element caused 4 by angular dependence can affect U-value. And this effect is not based on solar position, but solely on orientation compared to gravity. However, the SHGC and the VLT have big differences when it comes to the various incident angles of solar energy. The typical range of U-values vary from 0.49 BTU/h °F ft² (double glazing low-E, bronze tint) to 1.25 BTU/h °F ft² (single glazing, clear) and that of SHGC is from 0.39 (double glazing low -E, bronze tint) to 0.72 (single glazing, clear). Moreover, the typical VLT values are from 0.36 (double glazing low-E, bronze tint) to 0.71 (single glazing, clear) (Accent Windows, 2008). Solar Heat Gain Coefficient (SHGC) that is derived from solar heat gain (SHG) is one of the important thermal properties of glazing that need to be addressed, and it depends on solar radiation intensity, incident angle, number of panes, and type of coating (Karlsson 2001). Solar heat gain (SHG) refers to the temperature increase in a space that results from solar radiation and SHGC is the fraction of incident solar radiation admitted through a window, both directly transmitted and absorbed and subsequently released inward (Deal, Nemeth and DeBaille 1998). SHGC values range between 0 and 1, of which a lower value represents less solar heat that transmits through the window (Deal, Nemeth and DeBaille 1998). It is influenced by the position of the sun according to location, time of day, and orientation of glazing. As SHG provides passive heat to a space in winter, it is usually used for passive solar design for a building. In contrast to the benefit from SHG, it can be a factor for overheating to a space that requires cooling energy in summer. Therefore, the consideration of the balance between the solar heat gain and the climatic characteristic is important and the optimal SHGC of a fenestration varies depending on climate. An SHGC that is less than or equal to 0.4 is usually considered adequate for a window in most climates, except extremely cold or hot 5 climates. Low-e glass is popularly used in the contemporary building industry because it reflects heat back to its source reducing the SHG issues. The low-e glass has a special coating which makes the glass transmit short wave energy, allowing light in, while reflecting enough long wave energy to keep heat in the desired location (Accent Windows, 2008). In a very cold climate, a skin dominated building needs heating most of the year, thus the window should deliver heat from the outside to inside as much as possible, and at the same time, should not lose much of the heat to the outside. In regards to the aforementioned features, this means that the window should have high transmittance within the solar spectral region, high transmittance of solar energy, and as low-emittance as possible in the thermal spectral region (Karlsson 2001). The low-e glass that was mentioned previously plays a role for this climate. In contrast to the cold climate case, a building in a very hot climate has overheating problems which cause a huge cooling load. It is often acceptable, or even desired, to have a somewhat reduced transmittance within the visible region, so a lot of the solar energy can be blocked before it enters the building where it needs to be actively (expensively) cooled away (Karlsson 2001). The thermal portion of the spectrum should certainly be blocked as much as possible. In America, a window that has these properties is referred to as a solar control or spectrally selective window. 1.3. Nature of Sunlight Sunlight is a mixture of electromagnetic waves having different wavelengths. Each wavelength in the light produces a different color sensation in our eyes, from red to green to violet. The electric field vectors of natural light vibrate perpendicular to the axis of the beam. When the electric field vectors are restricted to a single plane by filtration, then the light is said to be polarized with respect to the direction of propagation and all 6 waves vibrate in the same plane (Olympus America Inc. 2011). Unpolarized incident light such as sunlight is polarized to a certain degree when it is reflected from a surface like water. The reflected portion is restricted to one plane. When light is transmitted from one material to another, the frequency of the light is unchanged, but the wavelength and wave speed can change (Young and Freedman 2007). The index of refraction (n) of an optical material is the ratio of the speed of light in vacuum to the speed in the material. Light always passes more slowly in a medium than in vacuum, so the value of n in anything other than vacuum is always greater than unity. Typical values of n are 1.33 for water, 1.52 for window glass, and 2.42 for diamond (Wikipedia). When light strikes a dielectric such as glass, the speed of the light slows down while the frequency stands still. In the dielectric, the wavelength of light is smaller than the wavelength in the vacuum. When the light passes through a medium which has different indexes of refraction, it will be separated into transmittance, reflectance and absorption. Here is the Fresnel equation (Figure 3) that describes the behavior of light when penetrating from one medium to another of a differing refractive index: 7 Figure 2: Variables used in the Fresnel equatio ns, Wikipedia Images, http://en.wikipedia.org/wiki/File:Fresnel1.svg When light moves from a medium of a given refractive index η1 into a second medium with refractive index n2, both reflection and refraction of the light may occur. An incident light ray PO strikes at point O the interface between two media of refractive indices n1 and n2. Part of the ray is reflected as ray OQ and part refracted as ray OS. The angles that the incident, reflected and refracted rays make to the normal of the interface are given as θ i, θ r and θ t, respectively. The relationship between these angles is given by the law of reflection: θ i = θ r ; and Snell’s law: sin(θ i)/sin(θ t) = n2/n 1. The fraction of the incident power that is reflected from the interface is given by the reflectance r and the fraction that is refracted is given by the transmittance t. The calculations of r and t depend on polarization of the incident ray (Wikipedia). Figure 3: Fresnel equations, Karlsson J, ‘Windows-Optical Perfo rmance and Energy Efficiency’, 2007, p.8 8 According to the equations above, s and p indicate polarization, where s indicates radiation normal to the plane of incidence, and p is parallel to the plane of incidence. At one particular angle for a given ni and nj, a particular polarization is purely transmitted with no reflection. This angle is known as Brewster's angle, and is around 56° for a glass medium in air or vacuum (Figure 4). If the incident angle of unpolarized light corresponds to this value, the reflected light from the surface is purely polarized. This statement is only true when the refractive indices of both materials are real numbers, as is the case for materials like air and glass. Figure 4: Brewster's angle, Wikipedia Images, http://en.wikipedia.org/wiki/File:Fresnel1.svg As a consequence of the conservation of energy, the transmission coefficient is given by Ts = 1 − R s and Tp = 1 − R p. (Eq. 5) When the Fresnel equation is applied to the light which passes through a glazing system, the calculation is more complex as the actual system has several different elements. 9 Therefore, the angular variation of the SHGC depends on the number of panes, type of coating, and the thickness of the panes and coatings. For ‘normal’ coating glass, the number of panes in the configuration is the important parameter, indicating that what governs the angle dependence is more a reflection effect than an absorption effect (Karlsoon and Roos 2000). Regarding glass coatings, the higher the index of refraction, n, of the coating, the higher the angle gets before the SHGC starts to decrease (Karlsoon and Roos 2000). The variation with angle of incidence depends mainly on which type of coating is used in the window and not on the coating thickness, but for some coatings, such as SS/TIN, there may be some variation with coating thickness (Karlsoon and Roos 2000). 1.4. ASHRAE 90.1 In this thesis, the ASHRAE 90.1 (ASHRAE STANDARD: Energy Standard for Buildings Except Low-Rise Residential Buildings) was reviewed with consideration to angle- dependent SHGC. In section 5, ASHRAE accounts for the detailed requirements of building envelope and there are three different methods to follow to meet the code: Prescriptive Path, Building Envelope Trade off Option, and Energy Cost Budget Method. The prescriptive path defines every single criterion for energy requirements such as assembly maximum U-factor, SHGC, and maximum glazing area, depending on the climate and the building type. The other paths concern the whole building energy simulation results and do not consider every single value of each properties or sections. Chapter 5 is the review of energy simulation programs with the angular dependence issues. To see how ASHRAE 90.1 applies angular dependence of glazing properties, the details in the prescriptive path were reviewed. Surprisingly, there is no consideration of the solar angle of incidence, as well as the orientation of the fenestrations, which makes a 10 huge difference in terms of solar heat gain. ASHRAE 90.1 only accounts for the SHGC at a normal angle. This means that the sun is assumed to be stationary and sunlight always penetrates a fenestration at a normal angle. According to this way of thinking, tilted fenestration always has a lower effective SHGC value than fenestration that is vertical because of the sun angles. However, the sun rise everyday and changes its position over time. If the accurate effect of the tilted glazing needs to be taken into account, it would be more complicated. Based on a discussion with ASHRAE officials, potential problems caused by ignorance of angle-dependent SHGC were recognized if an architect has a tilted glazing. Steve Ferguson, Assistant Manager of Standards at ASHRAE replied back to this concern with the description below. Given your description of tilted SHGC, I can see why 90.1 does not incorporate a tilted effect into the SHGC value. It would be near impossible to prescriptively describe the methodology to determine the effective SHGC within 90.1. Someone would likely need to write a standard on just how to determine the effective SHGC for tilted fenestration. If something like that existed, it would be easy for 90.1 to incorporate that methodology into 90.1. You are correct that 90.1 does not account for the solar angle for SHGC determination. I do know that ASHRAE is not currently writing a standard on this. (S Ferguson 2011, pers. comm. 26 September) Therefore, it was decided that the first stage of this thesis will concentrate on figuring out the way to calculate the effective SHGC for tilted fenestration. 1.5. Goals and Objectives This thesis focuses on the effect of angular dependence on DSHG of glazing, which is influenced by the position of the sun according to location, season, time of day, and orientation of the glazing. As the sun changes its position over time, SHGC should consider the incident angle of the sun's rays need for accurate calculation. NFRC only 11 defines SHGC at the normal angle of incidence and ASHRAE 90.1 does not account for the solar angle for SHGC determination. SHGC is actually defined as a sample with light hitting the glass at the normal to the surface, which never really happens physically unless it is a skylight, and then, only briefly. This circumstance leads us to overlook the time dependence factor of building envelope which influences the actual energy performance of buildings. Therefore, the angular dependent SHGC needs to be incorporated into the energy code or energy simulation programs. Actually, it is not straightforward to get the effect of SHGC at oblique angles of incidence in energy simulation programs. Among the numerous energy simulation tools, IES accounts for an angular-dependent factor in the SHGC value when it calculates cooling load but does not provide the specific values of SHGC based on the time of a day. Lawrence Berkeley National Laboratory’s Window6, which does the ISO 15099 (Thermal performance of windows, doors and shading devices -- Detailed calculations) calculation internally, accounts for the tilt effect when calculating convection, and also gives transmission properties for light on an angle to the surface but none of the energy simulation programs incorporate these detailed angular properties of glazing into their energy calculation. By analyzing the SHGC of inclined glazing with time-dependence of incidence, one estimates the optimal angle of glazing under energy code requirements in the early stage of design. SHGC can be measured by calorimetric methods but this gives no spectral information and is very time consuming (Karlsoon and Roos 2000). It can be theoretically calculated by ISO 9050 (Determination of light transmittance, solar direct transmittance, total solar energy transmittance, ultraviolet transmittance and related glazing factors), but it is only for near normal incidence. As ISO 9050 does not resolve the angular dependence, 12 SHGC of glazing with tilt effect should be obtained from the Fresnel equation that describes the behavior of light when moving between media of differing refractive indices. This basic physics equation was applied to the actual angular dependent SHGC of glazing calculation in the ASHRAE Handbook. In this book, Chapter 30 deals with fenestration and it provides the equation for solar angle, solar-optical properties of glazing and SHGC calculation. Based on the calculation method, the time-dependent values of SHGC can be obtained and analyzed. At the parametric study stage of this paper, a study is conducted to find the optimal angle for glazing selection in faceted building under ASHRAE requirements. This study shows the possible contribution of this effective DSHG research in designing patterns or geometry of building skin. Rhino and Grasshopper® were chosen as parametric tools for this study. Rhino is 3D modeling software which is a surface-based program and Grasshopper® is a graphical algorithm editor tightly integrated with Rhino’s 3 -D modeling tools. Grasshopper requires no knowledge of programming or scripting, but still allows designers to build form generators from simple to awe-inspiring (Davison 2012). Finally, parametric studies with the same process will be run in two zones: the northern zone (mostly heating) and the southern zone (mostly cooling). The resulting geometries of the façade compared to each other. 13 Chapter 2 Solar Heat Gain Coefficient Calculation To calculate effective SHGC, several steps need to be followed: determining incident solar irradiation, determining solar angle, and calculating the optical properties of glazing. In this chapter, the detailed calculation methods and previous research on angular dependence of SHGC is introduced. Based on these calculations, the angle- dependent SHGC is obtained. 2. . 14 2.1. Solar Radiation Incident on a Fenestration System When sunlight hits a glazing, it is partially transmitted, reflected, and absorbed by the glazing (Center for Sustainable Building Research 2011). The sum of these three values is unity. Solar heat gain through fenestration is calculated based on the amount of the transmitted and the absorbed solar radiation. The absorbed heat is reemitted to both the inside and the outside and the amount of the emitted heat can be obtained by multiplying N (U-factor divided by heat transfer coefficient of the glazing) and the absorbed portion of solar radiation (ASHRAE 2005). As the SHGC equation, Equation 6 shows, these values are angularly and spectrally selective. Figure 5 and Equation 6: Solar radiation incident on a fenestration, WHK, 2011 and SHGC Calculation, Chapter 31 Fenestration, ASHRAE Handbook-Fundamentals, 2005, p. 31.36 15 2.2. Determining Incident Solar Irradiation As the values which determine SHGC are spectrally selective, the SHGC calculation starts with determining incident solar flux. The flux of solar radiation on a surface normal (perpendicular) to the sun’s rays above the earth’s atmosphere at the mean earth -sun of 92.9 × 106 miles (Allen 1973) is 433 Btu/h•ft 2 (Iqbal 1983). This direct normal is reduced by the atmospheric coefficient as it approaches the Earth’s surface, generating EDN. The direct solar irradiance incident upon a single glass pane in direct sunlight is the product of the direct normal irradiation EDN and the cosine of the angle of incidence Ɵ between the incoming solar rays and a line normal to the surface (ASHRAE 2005). The earth’s orbital velocity varies throughout the year, so apparent solar time (AST), as determined by a solar time sundial, varies somewhat from the mean time kept by a clock running at a uniform rate. This variation, called the equation of time, is given in Table 7. The conversion between local standard time and solar time involves two steps: the equation of time is added to the local standard time, and then a longitude correction is added. This longitude correction is four minutes of time per degree difference between the local (site) longitude and the longitude of the local standard meridian for that time zone. Standard meridians are 60° for Atlantic Standard Time, 75° for Eastern Standard Time, 90° for Central Standard Time, 105° for Mountain Standard Time, 120° for Pacific Standard Time, 135° for Alaska Standard Time, and 150° for Hawaii- Aleutian Standard Time. Equation (10) relates apparent solar time (AST) to local standard time (LST) as follows: AST = LST + ET/60 + (LSM – LON)/15 Where, Because the earth’s equatorial plane is tilted at an angle of 23.45° to the orbital plane, the solar declination δ (the angle between the earth -sun line and the equatorial plane) varies throughout the y ear. This variation causes the changing seasons with their unequal periods of daylight and darkness. The following table contains the declination data for 21 st day of each month during the base year of 1964. It is more accurate to look up the actual declination in an astronomical or nautical almanac for the actual y ear and date (ASHRAE 2005). 16 Table 1: Equation of time values for 2011, Minasi M 2011, Equation of Time Calculator, Home of Technology Writer and Speaker Mark Minasi, accessed November 2011, <http://www.minasi.com/doeot.htm> 2.3. Determining Solar Angle One of the important variables for SHGC calculation is incident angle ɵ, depending on solar angle. The solar angle is defined by solar altitude (β) above the horizontal and solar azimuth ( ϕ) determined from the south. These two solar values depend on the local latitude (L), the solar declination (δ), and the hour angle (H) ( which is based on the apparent solar time, AST) (ASHRAE 2005). Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 1 -3m 18s -13m 28s -12m 13s -3m 44s 2m 56s 2m 5s -3m 56s -6m 17s 0m 8s 10m 27s 16m 22s 10m 46s 2 -3m 46s -13m 36s -12m 1s -3m 26s 3m 3s 1m 56s -4m 7s -6m 13s 0m 27s 10m 46s 16m 23s 10m 23s 3 -4m 14s -13m 43s -11m 48s -3m 9s 3m 9s 1m 46s -4m 18s -6m 8s 0m 47s 11m 4s 16m 23s 10m 0s 4 -4m 42s -13m 49s -11m 35s -2m 52s 3m 14s 1m 35s -4m 29s -6m 2s 1m 6s 11m 23s 16m 22s 9m 35s 5 -5m 9s -13m 55s -11m 21s -2m 34s 3m 19s 1m 25s -4m 39s -5m 56s 1m 26s 11m 40s 16m 20s 9m 11s 6 -5m 35s -13m 59s -11m 8s -2m 17s 3m 23s 1m 14s -4m 49s -5m 49s 1m 47s 11m 58s 16m 17s 8m 45s 7 -6m 2s -14m 3s -10m 53s -2m 1s 3m 27s 1m 3s -4m 59s -5m 42s 2m 7s 12m 15s 16m 14s 8m 20s 8 -6m 27s -14m 6s -10m 38s -1m 44s 3m 31s 0m 51s -5m 8s -5m 34s 2m 28s 12m 32s 16m 10s 7m 53s 9 -6m 52s -14m 8s -10m 23s -1m 28s 3m 33s 0m 39s -5m 17s -5m 25s 2m 49s 12m 48s 16m 5s 7m 27s 10 -7m 17s -14m 10s -10m 8s -1m 12s 3m 35s 0m 27s -5m 25s -5m 16s 3m 9s 13m 4s 15m 59s 6m 59s 11 -7m 41s -14m 11s -9m 52s -0m 56s 3m 37s 0m 15s -5m 33s -5m 7s 3m 30s 13m 20s 15m 52s 6m 32s 12 -8m 5s -14m 11s -9m 36s -0m 41s 3m 38s 0m 3s -5m 41s -4m 57s 3m 52s 13m 34s 15m 45s 6m 4s 13 -8m 28s -14m 10s -9m 20s -0m 25s 3m 38s -0m 9s -5m 48s -4m 46s 4m 13s 13m 49s 15m 36s 5m 36s 14 -8m 50s -14m 8s -9m 3s -0m 11s 3m 38s -0m 21s -5m 54s -4m 34s 4m 34s 14m 3s 15m 27s 5m 7s 15 -9m 12s -14m 6s -8m 47s 0m 3s 3m 38s -0m 34s -6m 0s -4m 23s 4m 56s 14m 16s 15m 17s 4m 38s 16 -9m 33s -14m 3s -8m 30s 0m 17s 3m 36s -0m 47s -6m 6s -4m 10s 5m 17s 14m 29s 15m 6s 4m 9s 17 -9m 53s -13m 59s -8m 12s 0m 31s 3m 34s -1m 0s -6m 11s -3m 57s 5m 38s 14m 41s 14m 54s 3m 40s 18 -10m 13s -13m 55s -7m 55s 0m 44s 3m 32s -1m 13s -6m 15s -3m 44s 6m 0s 14m 52s 14m 41s 3m 11s 19 -10m 32s -13m 50s -7m 37s 0m 57s 3m 29s -1m 26s -6m 19s -3m 30s 6m 21s 15m 3s 14m 28s 2m 41s 20 -10m 50s -13m 44s -7m 20s 1m 9s 3m 26s -1m 39s -6m 22s -3m 16s 6m 42s 15m 14s 14m 14s 2m 11s 21 -11m 7s -13m 38s -7m 2s 1m 21s 3m 22s -1m 52s -6m 25s -3m 1s 7m 3s 15m 23s 13m 58s 1m 42s 22 -11m 24s -13m 31s -6m 44s 1m 33s 3m 17s -2m 5s -6m 27s -2m 46s 7m 24s 15m 32s 13m 43s 1m 12s 23 -11m 40s -13m 23s -6m 26s 1m 44s 3m 12s -2m 18s -6m 29s -2m 30s 7m 45s 15m 40s 13m 26s 0m 42s 24 -11m 55s -13m 15s -6m 8s 1m 55s 3m 6s -2m 31s -6m 30s -2m 14s 8m 6s 15m 48s 13m 8s 0m 12s 25 -12m 9s -13m 6s -5m 50s 2m 5s 3m 0s -2m 43s -6m 31s -1m 57s 8m 27s 15m 55s 12m 50s -0m 16s 26 -12m 23s -12m 56s -5m 32s 2m 15s 2m 54s -2m 56s -6m 30s -1m 40s 8m 47s 16m 1s 12m 31s -0m 46s 27 -12m 36s -12m 46s -5m 14s 2m 24s 2m 47s -3m 8s -6m 30s -1m 23s 9m 8s 16m 6s 12m 12s -1m 15s 28 -12m 48s -12m 36s -4m 56s 2m 33s 2m 39s -3m 21s -6m 28s -1m 5s 9m 28s 16m 11s 11m 51s -1m 45s 29 -12m 59s -12m 24s -4m 38s 2m 41s 2m 31s -3m 33s -6m 26s -0m 47s 9m 48s 16m 15s 11m 30s -2m 14s 30 -13m 9s -4m 20s 2m 49s 2m 23s -3m 44s -6m 24s -0m 29s 10m 7s 16m 18s 11m 9s -2m 43s 31 -13m 19s -4m 2s 2m 14s -6m 21s -0m 10s 16m 20s -3m 11s 17 Table 2: Solar declination for 2011, Minasi M 2011, solar Declination Calculator, Home of Technology Writer and Speaker Mark Minasi, accessed November 2011, <http://www.minasi.com/doeot.htm> H = 15(AST – 12) (Eq. 6) (Eq. 7) cos ϕ β δ β (Eq. 8) Day JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 1 -23° 04' -17° 20' -7° 49' +4° 18' +14° 54' +21° 58' +23° 09' +18° 10' +8° 30' -2° 57' -14° 14' -21° 43' 2 -22° 59' -17° 03' -7° 26' +4° 42' +15° 12' +22° 06' +23° 05' +17° 55' +8° 09' -3° 20' -14° 34' -21° 52' 3 -22° 54' -16° 46' -7° 03' +5° 05' +15° 30' +22° 14' +23° 01' +17° 40' +7° 47' -3° 44' -14° 53' -22° 01' 4 -22° 48' -16° 28' -6° 40' +5° 28' +15° 47' +22° 22' +22° 56' +17° 24' +7° 25' -4° 07' -15° 11' -22° 10' 5 -22° 42' -16° 10' -6° 17' +5° 51' +16° 05' +22° 29' +22° 51' +17° 08' +7° 03' -4° 30' -15° 30' -22° 18' 6 -22° 36' -15° 52' -5° 54' +6° 13' +16° 22' +22° 35' +22° 45' +16° 52' +6° 40' -4° 53' -15° 48' -22° 25' 7 -22° 28' -15° 34' -5° 30' +6° 36' +16° 39' +22° 42' +22° 39' +16° 36' +6° 18' -5° 16' -16° 06' -22° 32' 8 -22° 21' -15° 15' -5° 07' +6° 59' +16° 55' +22° 47' +22° 33' +16° 19' +5° 56' -5° 39' -16° 24' -22° 39' 9 -22° 13' -14° 56' -4° 44' +7° 21' +17° 12' +22° 53' +22° 26' +16° 02' +5° 33' -6° 02' -16° 41' -22° 46' 10 -22° 05' -14° 37' -4° 20' +7° 43' +17° 27' +22° 58' +22° 19' +15° 45' +5° 10' -6° 25' -16° 58' -22° 52' 11 -21° 56' -14° 18' -3° 57' +8° 07' +17° 43' +23° 02' +22° 11' +15° 27' +4° 48' -6° 48' -17° 15' -22° 57' 12 -21° 47' -13° 58' -3° 33' +8° 28' +17° 59' +23° 07' +22° 04' +15° 10' +4° 25' -7° 10' -17° 32' -23° 02' 13 -21° 37' -13° 38' -3° 10' +8° 50' +18° 14' +23° 11' +21° 55' +14° 52' +4° 02' -7° 32' -17° 48' -23° 07' 14 -21° 27' -13° 18' -2° 46' +9° 11' +18° 29' +23° 14' +21° 46' +14° 33' +3° 39' -7° 55' -18° 04' -23° 11' 15 -21° 16' -12° 58' -2° 22' +9° 33' +18° 43' +23° 17' +21° 37' +14° 15' +3° 16' -8° 18' -18° 20' -23° 14' 16 -21° 06' -12° 37' -1° 59' +9° 54' +18° 58' +23° 20' +21° 28' +13° 56' +2° 53' -8° 40' -18° 35' -23° 17' 17 -20° 54' -12° 16' -1° 35' +10° 16' +19° 11' +23° 22' +21° 18' +13° 37' +2° 30' -9° 02' -18° 50' -23° 20' 18 -20° 42' -11° 55' -1° 11' +10° 37' +19° 25' +23° 24' +21° 08' +13° 18' +2° 06' -9° 24' -19° 05' -23° 22' 19 -20° 30' -11° 34' -0° 48' +10° 58' +19° 38' +23° 25' +20° 58' +12° 59' +1° 43' -9° 45' -19° 19' -23° 24' 20 -20° 18' -11° 13' -0° 24' +11° 19' +19° 51' +23° 26' +20° 47' +12° 39' +1° 20' -10° 07' -19° 33' -23° 25' 21 -20° 05' -10° 52' 0° 00' +11° 39' +20° 04' +23° 26' +20° 36' +12° 19' +0° 57' -10° 29' -19° 47' -23° 26' 22 -19° 52' -10° 30' +0° 24' +12° 00' +20° 16' +23° 26' +20° 24' +11° 59' +0° 33' -10° 50' -20° 00' -23° 26' 23 -19° 38' -10° 08' +0° 47' +12° 20' +20° 28' +23° 26' +20° 12' +11° 39' +0° 10' -11° 12' -20° 13' -23° 26' 24 -19° 24' -9° 46' +1° 11' +12° 40' +20° 39' +23° 25' +20° 00' +11° 19' -0° 14' -11° 33' -20° 26' -23° 26' 25 -19° 10' -9° 24' +1° 35' +13° 00' +20° 50' +23° 24' +19° 47' +10° 58' -0° 37' -11° 54' -20° 38' -23° 25' 26 -18° 55' -9° 02' +1° 58' +13° 19' +21° 01' +23° 23' +19° 34' +10° 38' -1° 00' -12° 14' -20° 50' -23° 23' 27 -18° 40' -8° 39' +2° 22' +13° 38' +21° 12' +23° 21' +19° 21' +10° 17' -1° 24' -12° 35' -21° 01' -23° 21' 28 -18° 25' -8° 17' +2° 45' +13° 58' +21° 22' +23° 19' +19° 08' +9° 56' -1° 47' -12° 55' -21° 12' -23° 19' 29 -18° 09' -8° 03' +3° 09' +14° 16' +21° 31' +23° 16' +18° 54' +9° 35' -2° 10' -13° 15' -21° 23' -23° 16' 30 -17° 53' +3° 32' +14° 35' +21° 41' +23° 13' +18° 40' +9° 13' -2° 34' -13° 35' -21° 33' -23° 12' 31 -17° 37' +3° 55' +21° 50' +18° 25' +8° 52' -13° 55' -23° 08' 18 Figure 6: Solar angles for vertical and horizontal surfaces, Chapter 31 Fenestration, ASHRAE Handbook-Fundamentals, 2005, p. 31.16 Figure 6 shows the solar position angles and incident angles for horizontal and vertical surfaces. Line OQ leads to the sun, the north-south line is NOS, and the east-west line is EOW. Line OV is perpendicular to the horizontal plane in which the solar azimuth φ (angle HOS) and the surface azimuth ψ (angle POS) are located. Angle HOP is the surface solar azimuth γ, defined as γ =  - (Eq. 9) The solar azimuth φ is positive for afternoon hours and negative for morning hours. Likewise, surfaces that face west have a positive surface azimuth ψ; those facing east have a negative surface azimuth. If γ is greater than 90° or less than – 90°, the surface is in the shade. The angle of incidence θ for any surface is defined as the angle between the incoming so lar rays and a line normal to that surface. (ASHRAE 2005) The incident angle can be obtained by the equations (8) and (9) based on the solar altitude (β), the solar azimuth ( ) and tilt angle of a surface (Σ). cos ɵ = cosβ cosγ sinΣ + sinβ cosΣ (Eq. 10) 19 2.4. Solar Optical Properties of Glazing ISO 9050 deals with the determining procedure of solar-optical properties of a glazing in buildings. These are the wavelength-integrated transmittance, reflectance, and absorptance of the glazing to incident solar radiation which are determined for almost normal radiation incidence. The total solar energy transmittance is the sum of the solar direct transmittance (τ) and the secondary heat transfer factor towards the inside (N α), the latter resulting from heat transfer by convection and long wave IR-radiation of that part of the incident solar radiation which has been absorbed by the glazing. The solar direct transmittance of glazing will be obtained using the following formula: = τ (Eq. 11) Where τ The solar direct reflectance ρ of glazing will be calculated using the following formula: ρ = (Eq. 12) Where 20 2.5. Angular Dependence of Glazing Optical Properties The optical properties of glazing are usually regarded to be only at normal angle because angular integrated calculations are very time-consuming and complicated when it comes to complex glazing system (Karlsson and Roos 2000). However, in reality, they are significantly various with angle of incidence. Even the National Fenestration Rating Council (NFRC) only defines the properties at normal incidence. In their publication, NFRC 200-2010 (Determining Fenestration Product Solar Heat Gain Coefficient and Visible Transmittance at Normal Incidence), they mention this issue as: While solar radiation rarely enters a fenestration product at normal incidence, SHGC and VT at near normal angles of incidence (less than 30° off normal) are ty pically very similar to those at normal incidence; for other angles, the SHGC and VT at normal can be used, to first order, as an indicator of the relative magnitude of SHG and VT (ASHRAE 2005). The optical properties of glazing depend on the angle of incidence (ASHRAE 2005) As Figure 7 shows, the variation with incident angle of three different solar-optical properties for glazing becomes significant at 40° and drastically changes by 90°. Figure 7 deals with comparison of each property in different thickness and types of glass. The overall configurations of the curve are similar in the graphs but none of them has an identical angular dependence. For coated glasses or for multiple-pane glazing systems, this difference is more pronounced (ASHRAE 2005). 21 Figure 7: Variatio ns with incident angle of solar-optical properties for (A) Double-Strength Sheet Glass, (B) Clear Plate Glass, and (C) Heat-Absorbing Plate Glass, Chapter 31 Fenestration, ASHRAE Handbook-Fundamentals, 2005, p.31.20 The ignorance of angular dependency of glazing properties can lead to the inaccurate or wrong result in building simulation program. Theoretically, angular resolved properties are well defined by the Fresnel equations and it is rigorous as long as the thickness of all the coatings and their optical constants are known (Karlsson 2001). This feature becomes critical when it comes with coated glazing. Here is a description of Window optics from the Lawrence Berkeley National Laboratory (LBNL) in regards to angle dependent optical properties: Currently ISO 9050 does not include procedures for measuring or extrapolating angle dependence of coated glass. Perhaps a review of the ADOPT work and other key papers on the subject would lead to something going into the standard. It is actually very important. Proper angle dependence can have a much larger effect than say choice of solar spectrum (Windows and Day lighting Group). This paragraph shows that LBNL also admit their ignorance of the angular dependency in optical properties but highly state the necessity of consideration to the issue. 22 2.6. Angular Dependent SHGC in Previous Research There are ways of calculating or measuring the g-value (SHGC), but the g-value depends on the angle of incidence, so these procedures need to be performed for different angles of incidence (Karlsson and Roos 2000). The g-value can be measured by calorimetric methods but this gives no spectral information and is very time consuming. The calculation can be performed using the ISO 9050 standard (Karlsson and Roos 2000). As it is not straightforward to obtain g-value (or its American equivalent, SHGC) with oblique angles, many people have been using empirical formulas in previous research. Among the several empirical methods, a frequently used model is a tangent or cosine based equation, (Montecchi and Polato, 1995; Schultz and Svendsen, 1998), such as: g = g (0) (1 – tan ( ɵ /2)) (Eq. 13) where u is the angle of incidence and x is a variable exponent (x equals about 4 for most windows) and g(0) is the g-value at normal incidence. This model fits well at low angles and for a few windows also at high angles of incidence. The model can also be used with the exponent x as a categorization parameter with different exponents for different window types (Montecchi and Polato, 1995) but the degree of freedom is limited to give only one inflexion point (Karlsson and Roos 2000). The model in the previous paragraph is limited because it is oversimplified. The other recent empirical formula was developed by J. Karlsson. In his paper, he proposed a model where a polynomial was fitted to the angle dependence of the direct solar transmittance for single glazed, coated panes as a new empirical method. (Eq. 14) Where a +b+ c = 1 and z=q/90. 23 p refers to the number of panes in the configuration and q means category parameter. (1~10) These empirical formulas are simple and a reasonably good fit to the actual SHGC value, with the exception of high angles of incidence. Therefore, we need to go for ‘bulk method’ (Karlsson and Roos 2000) which treats each glazing s eparately. This approach normally needs R and T-values at normal incidence for each wavelength. From the R and T-data of the actual glazing, “pseudo” optical constants are extracted for the equivalent glazing, which is then used to represent the angle dependence profiling of the actual glazing. After that, the procedure is the same as for exact Fresnel calculation using ISO 9050 to obtain the window optical performance at the desired angles of incidence (Karlsson and Roos 2000). 2.7. Detailed Optical Property Calculation 2.7.1. Optical Properties of Single Glazing layers Figure 9 is the diagram which shows the behavior of optical properties. Figure 8: Optical properties of a single glazing layer, Chapter 31 Fenestration, ASHRAE Handbook-Fundamentals, 2005, p. 31.20 The layer has a thickness d and is characterized by a surface reflectivity and transmissivity, and τ, for each of the two surfaces (denoted f and b in the figure) and an absorptivity, α, which is a volumetric property of the material (assumed of uniform composition). The transmittance T and front reflectance R f of a lay er (as 24 opposed to a surface) contain the effects of multiple reflections between the two surfaces of the layer, as indicated in Figure 8, as well as the effects of absorption during the passage through the layer (one or more times), due to the volume absorptivity α. The same is true of the back reflectance R b, which is the reflectance of the layer for radiation incident on back side b and which is not illustrated in the figure. For non-normal incidence, surface reflectances are in general different for the two possible polarizations of light, conventionally denoted s and p. We distinguish these below by a subscript μ (= s,p) on the surface reflectance. The transmittance and reflectances are given by (Eq. 15) (Eq. 16) (Eq. 17) where ζ is the angle at which radiation incident at angle θ propagates within the glazing layer (the refracted angle). Since sunlight is unpolarized, the transmittance and reflectances of an isolated glazing layer are then calculated from (Eq. 18) (Eq. 19) (Eq. 20) The transmittance is the same for incident radiation incident (of a given polarization) on either surface. Front and back reflectance, however, may differ. 2.7.2. Uncoated Glass For uncoated glazing, the interface reflectivity of the two surfaces are the same and may be determined from the Fresnel equations: (Eq. 21) (Eq. 22) 25 For uncoated glazings, the interface reflectivities of the two surfaces are the same and may be determined from the Fresnel equations: (Eq. 23) For uncoated glazing, the interface reflectivity of the two surfaces are the same and may be determined from the Fresnel equations: 2.7.3. Coated Glass While in principle the equations in the preceding sections could be used to calculate the properties of coated glazing, this is not currently practical. To obtain the necessary basic information about the structure of complex coatings would require spectrophotometric measurements at angles other than normal incidence. Coated glazing properties should vary from these estimates by no more than ± 20% at 60° incidence. The spectral transmittance and reflectance at any incident angle are approximated from those at normal incidence by (Eq. 24) (Eq. 25) (Eq. 26) (Eq. 27) The constants in Equations (56) and (57) are selected from the entries in Table 12 appropriate to the value of the spectrally average transmittance at normal incidence, T(0). Because Equations (54) and (55) make wavelength -independent modifications to the properties at normal incidence, the spectral averaging may be done first, y ielding (ASHRAE 2005). (Eq. 28) (Eq. 29) 26 2.8. Detailed SHGC Calculation A single layer of uncoated 1/8 in. clear glass was chosen. It is suitable for use in calculations which account selective glazing that has different properties in the visible and NIR (Near Infrared) regions. The calculation begins with the spectral transmittance and reflectance of the glass which can be obtained from NFRC Spectral Data Library. Wav elength, nm Wav elength, nm Figure 9: Two band model in spectral data library 1 and library2, Chapter 31 Fenestration, ASHRAE Handbook-Fundamentals, 2005, p. 31.22 ASHRAE Handbook uses the “2 -band” model. In the graphs as the variation of the values with wavelength is not very great. One of the bands covers the visible region (320nm to 780nm) and the other does the near infrared (NIR) region (780nm to 2500nm). At the first stage of the calculation, the normal incidence properties of the glass were defined from the spectral data in the graphs. T (0, vis) = 0.876, R (0, vis) = 0.081, T (0, NIR) = 0.791, and R (0, NIR) = 0.069 The Equation1 yields P. (Eq. 1) P= [T(0, λ)]² - [R(0, λ)]² + 2R(0, λ) + 1 P (vis) = (0.876)² - (0.081)² + 2(0.081) + 1 = 1.923 and P (NIR) = (0. 791)² - (0. 069)² + 2(0. 069) + 1 = 1.759 27 From the Equation2, surface reflectance can be obtained. (Eq. 2) ρ(0, λ) = ρ (0, vis) = , ρ(0, NIR) = The equation3 provides the refractive index. (Eq.3) n(λ) = n (vis) = = 1.531 and n(NIR) = = 1.508 The equation4 gives the value α(λ). (Eq.4) α(λ) = α (vis) = 0.0147 and α(NIR) = 0.0506 All of these parameters are necessary for determining the optical properties. Let’s find out the incident angle of the glazing according to a possible location and time. At 3:00 P.M. Pacific daylight time on July 21st in Los Angeles, CA. LST = 15 Latitude (L) = 33.93N Longitude = 118.38W Local standard median of the pacific time zone = 120° Equation of time at July = -6.2 (Eq. 5) AST = LST + ET/60 + (LSM – LON)/15 AST = 15 + -6.2/60 + (120-118.38)/15 = 16.5167 (Eq. 6) H = 15(AST – 12) 28 H = 15(16.5167 – 12) = 67.75° Solar declination on July 21 st ° from Table 7 in ASHRAE Handbook Thus, by Equation6, (Eq.7) sinβ = cosLcos  H Sinβ = cos(33.93°)cos(20.60°)cos(67.75°) = 0.2941 β = 17.10° (Eq.8) cosΦ = cosΦ = ° ° ° ° ° = -0.2376 Φ = 103.74° Incident angle ( ɵ) at a vertical (Σ =0) window facing south (Ψ =0) is defined by Equation9 (Eq. 9) cos ɵ = cosβ cosγ sinΣ + sinβ cosΣ cos ɵ = cos (17.10°) cos(103.74°) sin(0°) + sin(17.10°) cos(0° ) = sin(17.10° ) =0.2940 ɵ = 72.90° Equation 10 gives (Eq. 10) sin ɵ = nsin and ζ = arc sin( ) ζ (vis) = arc sin( ) = 38.63° ζ (NIR) = arc sin( ) = 39.33° For polarizations, Equation 11 gives s(72.9°,vis), s(72.9°,NIR), p(72.9°,vis) and p(72.9°,NIR) (Eq. 11) ρs( ɵ,λ) =( )², ρp( ɵ,λ) =( )² 29 Ρs (72.9°,vis) = ( )² = ( )² = 0.3664 ρ p(72.9°,vis) = ( )² =( )² = 0.0723 ρs (72.9°,NIR) = ( )² = ( )² = 0.3568 ρp (72.9°, NIR) = ( )² =( )² = 0.0736 From Equation12, s(72.9°,vis), s(72.9°,NIR), p(72.9°,vis) and p(72.9°,NIR) can be obtained (Eq. 12) μ( ɵ, λ) + μ( ɵ, λ) =1 s (72.9° ,vis) = 0.6336 s (72.9° ,NIR) = 0.6432 p (72.9°,vis) = 0.9277 p(72.9°,NIR) = 0.9264 Putting these values into Equations 12 through 14 gives for the transmittances and reflectances for each polarization: (Eq. 13) (Eq. 14) sT (72.9°,vis) = ° ° = = 0.448 sR (72.9°,vis) = 0.3664+0.3664 * 0.448 * ° = 0.522 sT (72.9°,NIR) = ° ° = = 0.375 sR (72.9°,NIR) = 0.3568+0.3568 * ° = 0.753 30 pT (72.9°,vis) = ° ° = = 0.822 pR (72.9°,vis) = 0.0723 + 0.0723 * ° = 0.141 pT (72.9°,NIR) = ° ° = = 0.712 pR(72.9°,NIR) = 0.0736 + 0.0736 * ° =0.155 From Equation 15, the parameters which is necessary for SHGC calculation are finally obtained (Eq. 15) T( ɵ,λ) = [ sT( ɵ,λ) + pT( ɵ,λ) ] T (72.9°,vis) = [0.448+ 0.822] = 0.635 R (72.9°,vis) = [0.522+ 0.141] = 0.332 T (72.9°,NIR) = [0.375+ 0.712] = 0.544 R (72.9°,NIR) = [0.753+ 0.155] = 0.454 (Eq. 16) SHGC( ɵ,λ) = T( ɵ,λ) + NA( ɵ,λ) N = = (at low wind speeds) = 0.867 SHGC (72.9°,vis) = 0.635 + 0.867 * (1-0.635-0.332) = 0.664 SHGC (72.9°,NIR) = 0.544 + 0.867 * (1-0.544-0.454) = 0.546 Equation 17 implies a wavelength-averaged solar heat gain coefficient. (Eq. 17) SHGC ( ɵ) = SHGC ( °) = ° ° 31 If we use simple-weighed method, the result is: SHGC ( °) = (ASHRAE 2005) 32 Chapter 3 Direct Solar Heat Gain Calculation This chapter introduces direct solar heat gain calculation through glazing based on perpendicular direct incident solar radiation and the effective SHGC. These two variables for the calculation are determined by incident angle, which accounts for the specific location, time, and surface azimuth. A master spreadsheet was developed and includes all of the variables to calculate the direct solar heat gain. 3. . 33 3.1. Direct Solar Heat Gain Calculation Peak solar gain through a window and its associated cooling load can be a major component in determining the application and evaluation of low-energy systems (Waddell 2010). It is therefore vital to predict the solar gain and the time when peaks occur accurately in order to make decisions about the façade measurements and system selection even at a conceptual design phase (Waddell 2010). In the previous chapter, the calculation of effective SHGC of glazing was introduced. SHGC is the one of the main factors for Direct Solar Heat Gain (DSHG) and DSHG is directly related to cooling load estimation which always comes with energy consumption issues. The solar energy flow through a fenestration may be split into two parts, opaque and glazing portions, q op and qs, respectively, as given in Equation 45 (ASHRAE 2005). Q sol = A opqop + Asqs (Eq. 45) where, Aop refers the area of the opaque part and As means the area of the glazing. The glazing portion of the solar energy can be divided into three parts as well: direct beam radiation (q b), diffuse sky radiation (qd), and radiation reflected from the ground (q r). Therefore, the equation for incident solar flux to glazing is defined as: qs = q b + qd + q r (Eq. 46) As direct normal radiation is one of the main contributors of solar heat gain through fenestration, this thesis only focuses on DSHG. It can be obtained by multiplying direct incident solar radiation (E D) by SHGC. E D can be calculated by direct normal solar radiation (E DN) and cosine Ɵ. Ɵ represents the angle of incidence. Figure 10 shows the effect of incident angle on incident solar radiation. After all, DSHG is obtained from E DN , cos Ɵ, SHGC ( Ɵ). qb = E DN * cos Ɵ * SHGC( Ɵ) (Eq. 97) 34 In this process, one can realize that the incident angle matters with double effect as cosine and SHGC are influenced by the incident angle. In other words, if we do not consider angle-dependence in DSHG, it can make for a huge difference from reality. Figure 10: Cosine law and surface incidence 3.2. Spreadsheet for Direct Solar Heat Gain Calculation As the thesis mentioned previously, DSHG Calculation is not straight forward in building codes and energy simulation software when the project has faceted and curvilinear building facades where the glazing is not necessarily vertical. This can lead to errors in the building performance prediction. To improve DSHG calculation, a master spreadsheet that includes incident angle calculation based on the specific location, time and surface azimuth was developed. The effect of incident angle was reflected in direct solar heat calculation based on perpendicular direct incident solar radiation and the effective SHGC to produce the spreadsheet. Using this spreadsheet, one can predict the amount of DSHG from each area of tilted glazing, with time-dependence throughout the year. The spreadsheet calculation was conducted from 5am to 7pm in January to December on an hourly-basis. It consists of ten different tables and each table refers to AST, the hour 35 angle H, solar altitude, solar azimuth, incident angle, surface solar azimuth, direct solar radiation, cosine (incident angle, Ɵ), SHGC, and DSHG in that order. The last table with colored cells represents the DSHG which the spreadsheet ultimately pursues to calculate. Figure 11 is the overall configuration of the spreadsheet. Figure 11: Master spreadsheet (see Figure 86 as a supplemental file) The effect of incident angle was reflected in direct solar heat calculation based on direct normal solar radiation (EDN) and the effective SHGC in the spreadsheet. Figure 12 is the DSHG values in monthly average, so that one can easily figure out the DSHG difference among the month, and the specific time of day. In Figure 12, inputs are in yellow -green cells: location (Altitude, Latitude), orientation (0° means south, 90° is west, 180° refers to north, and 270° represents east) as 360 degrees. Tilt (0° means horizontal, 90° refers to vertical, and over 90° represents tilt toward outside of the building) and effective SHGC from previous work are also inputs. The outputs represent hourly-base DSHGs value and they also provide the average for a year and one can find the peak gain as well. The cells are colored with light yellow to dark drown; lighter colors mean higher values of DSHG and white cells show no direct solar heat gain in that time. The output configuration of the master spreadsheet looks similar to an Ecotect solar gain analysis 36 data but as mentioned previously, it is different. The difference will be explained with a detailed description in Chapter 5 of this thesis. Figure 12: Spreadsheet results, South Façade, Phoenix, AZ 3.3. Simple Case Comparison in the Spreadsheet Figure 13: Two different shaped-buildings in Rhino and Grasshopper 37 A simple DSHG comparison was conducted with the spreadsheet. Assume that these are buildings in Phoenix, Arizona: a typical rectangular box-shaped building and a truncated pyramid-shaped building (Figure 13). The image shows that the total area of four sides in both buildings stays the same by using rhino and grasshopper. Along with the area constraints, the tilt angle of the truncated pyramid-shape building was extracted from grasshopper components and the value is about 15°. This angle of tilt was input to the spreadsheet to see the DSHG difference in this climate. The detailed knowledge and applications of Rhino and Grasshopper to this research will be explained in Chapter 5. The following spreadsheet images show the DSHG configuration throughout a year, representing the comparison between vertical glazing (the table in the left) and 15° tilted glazing (the table on the right) for each facade. Figure 14: South facades 38 Figure 15: West facades Figure 16: North facades Figure 17: East facades By using this spreadsheet, we can clearly see the DSHG difference between the vertical glazing and 15 degree tilted glazing and the numerical values were compared in the graph below (Figure 18). 39 Figure 18: DSHG comparison: vertical glazing and 15 degree tilted glazing In Figure 18, even though the glazing areas are the same, if the glazing is tilted, the direct solar heat gain value is different. From this result, there can be a mini conclusion: the duration of the time which the south facade gets direct solar radiation is longer than the 15 degree-sloped glazing. Likewise, summer and winter month DSHG values are larger in 15 tilted glazing than that of vertical. Therefore, the 15 degree tilted glazing in Arizona mostly has worse energy performance, as it gives the building a larger DSHG over a year which is a main factor in the cooling load. However, this result is only applied to Phoenix, Arizona and not for other locations. There might be different DSHG configuration in different locations. At the same time, the large DSHG can be of merit for some specific climates which need heating or regions which experience really cold temperatures during winter, which consumes a huge amount of energy for heating. Therefore, we need to look at the DSHG configuration more thoroughly and the spreadsheet allows us to have a better idea of overall solar heat gain behavior of the glazing based on the angle of tilt and orientation. 40 3.4. ASHRAE Baseline and Spreadsheet Calculation in Different Climates 3.4.1. Prescriptive Building Envelope Option in ASHRAE As mentioned in Chapter 1, ASHRAE Standard 90.1 provides building envelope requirements for a specific climate zone. The North America Region consists of eight different climate zones and ASHRAE assigned the assembly maximum value of glazing properties according to the climate. Among the zones, four different regions were chosen to represent the types of hot-arid, hot humid, cool and temperate climates: Phoenix, Arizona; Miami, Florida; Minneapolis, Minnesota; and New York City, New York. Although somewhat arbitrary, this choice of climate samples offers the possibility of comparing diverse environments and their effects on architectural principles and building elements (Olgyay 1963). The following Tables are from ASHRAE 90.1 which show the fenestration assembly maximum SHGC in each climate zone. Table 3: Building Envelope Requirement for Climate Zone2 (Miami, FL), Section 5 Building Envelope, ASHRAE 90.1, 2007, p.20 41 Table 4: Building Envelope Requirement for Climate Zone3 (Phoenix, AZ), Sectio n 5 Building Envelope, ASHRAE 90.1, 2007, p.21 Table 5: Building Envelope Requirement for Climate Zone5 and 6 (New York City, NY and Minneapolis, MN), Section 5 Building Envelope, ASHRAE 90.1, 2007, p.23-24 As the tables indicate above, the SHGC requirement for fenestration differs in each climate zone. In Phoenix and Miami, the maximum SHGC of the glazing system is 0.25 42 and 0.4 for New York City and Minneapolis. In order to compare the spreadsheet calculation result among different angles of tilted glazing, specific glazing system properties need to be defined to apply the effective SHGC to the spreadsheet. Therefore, two types of low-e double glazing systems were selected in Window6 with consideration to required maximum of SHGC: 0.25 and 0.4. Figure 19 and 20 show the sample glazing system assemblies and their angular properties in Window6. As introduced in Chapter2, the effective SHGC of uncoated glazing can be calculated by existing equations but in case of low-e coated glazing, the Window6 program is required to get the accurate effective SHGC values for direct solar heat gain calculation. Based on these SHGC values, spreadsheet calculations were conducted and the results were compared or analyzed. Figure 19: Low-e double glazing system angular properties in Windows6 (SHGC(0°) = 0.248) 43 Figure 20: Low-e double glazing system angular properties in Windows6 (SHGC(0°) = 0.399) 3.4.2. Spreadsheet Calculation Results in Four Climate Zones Figure 21: Tilt angle definitio n diagram 44 Spreadsheet Calculations were done with four different orientations and five different angles of tilt. Figure 21 shows the definition of tilt in a diagram. One of the tilt angles is 0° which is typical glazing with no tilt and the others would be tilted towards the outside or inside Figures 22 to 25 are the spreadsheet results when ASHRAE baseline SHGCs were applied (Phoenix and Miami: 0.248, Minneapolis and New York City: 0.399.) As indicated, column means orientation (south to east) and row means angle of tilt (-30°, - 15°, 0°, 15° and 30°.) Figure 22: Spreadsheet result, Phoenix, Arizona 45 Figure 23: Spreadsheet result, Miami, Florida Figure 24: Spreadsheet result, Minneapolis, Minnesota 46 Figure 25: Spreadsheet result, New York City, New York In general, when the glazing was tilted outwards, they get less direct solar heat gain compared to glazing with no tilt. In contrast to outward tilted glazing, inward tilted glazing has higher value of direct solar heat gain than the vertical glazing with 0°tilt. The outward tilt effect cuts the direct sun penetration on south faces (Figure 22 to 25). The effect allows west and east fenestration to receive less or no direct sunlight at noon time but if it is an inward tilt, they get the light for much longer period of time. The North façade originally has direct solar heat gain in early morning or late afternoon but inward tilt lets the façade have direct sun all day during the summer period which is undesirable as most of the climates need cooling over the summer. In the comparison between Phoenix and Miami, most south glazing in Miami gets receives more solar heat gain and also receives direct sunlight for a longer period of time. An inward tilt on the north façade in Phoenix performs better than Miami as it has less direct sun during summer. Minneapolis and New York have similar solar heat gain 47 patterns which are shown in table 26 and 27. The west and east glazing system behaves almost the same in both climates but Minneapolis’ south glazing with outward tilt gets less direct solar heat gain than New York’s. However, inward tilt of the north façade in Minneapolis receives direct sunlight over wider range of time, especially in summer. As the spreadsheet results clearly show, the angular dependence of direct solar heat gain makes a significant difference between the various angles, orientation and the direction of tilt. If ASHRAE does not consider these effects on the prescriptive building envelope requirements, it would cause serious error when architects and building engineers design their building to meet the energy performance or simulate the whole building energy criteria. The following analysis is the numeric comparison based on the spreadsheet calculation. 3.4.3. Direct Solar Heat Gain Analysis in Four Climate Zones Based on the spreadsheet calculation with four different orientations and five different tilt angles, the results were analyzed for the total DSHG, the difference between winter peak and summer peak. The total DSHG results show the differences between glazing with different angles of tilt or orientations as accumulated values throughout a year. The peak difference indicates one possible way to observe the DSHG data in terms of the offset effect of DSHG and efficiency in sizing heating system. DSHG has merit in terms of building energy performance as it can reduce heating load in winter, and the size of energy system is determined with regards to the worst (peak) case, but the cooling load might be higher if a building has a lot of DSHG in summer. Therefore, the large difference between winter peak and summer peak is preferable as the DSHG can offset a certain amount of heating load. The difference is winter peak minus summer peak so 48 that the larger, the better performance in winter as it gives a large amount of solar heat gain in winter whereas summer does not get much amount of solar heat gain. The peak DSHG in summer is directly related to cooling load as the HVAC system size is determined based on the calculated load in worst case scenario.  Phoenix, Arizona Figure 26: Total direct solar heat gain of glazing in different angle of tilt , Phoenix, AZ Figure 26 represents the total direct solar heat gain value of the glazing with 0.248 SHGC, similar to ASHRAE requirement, 0.25. The yellow green bar is vertical glazing with no tilt. If the glazing is tilted outward, it gives less direct solar heat gain throughout the year. In contrast to that, an inward tilt causes more direct solar heat gain in every orientation. South, West and East fenestrations have similar increasing total solar heat gains if the surface is tilted from outward to inward, but the north has a different 49 increase. Figure 26 clearly expresses that when it is tilted inward, from 0° (vertical) to 15°, the increasing direct solar heat gain was not that much. But from 15° to 30°, it increased a great deal. From this tendency, one can realize that the greater degree of inward tilt would cause significant increase in direct solar heat gain of a north-facing façade. Figure 27 : Winter peak - summer peak, Phoenix, Arizona In figure 27, differences between winter peak and summer peak are shown. The south fenestration is the best as it has much larger value than the other facades. Vertical glazing (with no tilt) is preferable for the south. The tendency of the difference between winter peak and summer peak of east, west and north behaves similarly. An inward tilt is not desirable in the three orientations. The greater outward-tilt glazing is the better for winter energy-efficiency for all of the orientations except the south in Phoenix, Arizona. Based on figure 27, one can figure out that the south fenestration always has positive (-)30 tilt (-)15 tilt Vertical 15 tilt 30 tilt South 20.28511209 33.06080258 39.50232479 30.56305286 14.87456956 West -1.589448751 -5.678940743 -10.33244431 -17.26466599 -22.0429933 North -5.832395396 -7.253182481 -8.179677165 -10.12132887 -14.73259256 East -6.964346272 -9.070026615 -14.16508583 -18.6414588 -25.55661465 -30 -20 -10 0 10 20 30 40 50 Winter Peak - Summer Peak (BTU/ft^2) Winter Peak - Summer Peak 50 winter peak minus summer peak, which means that winter peak is always larger than summer peak. In contrast, the other orientations always negative values of the peak difference and it means that their summer peak is always larger than winter peak. Figure 28: Summer DSHG peak, Phoenix, AZ Figure 28 shows the summer DSHC peak for each tilted glazing with different orientations. In general, all of the gains for different orientations gradually increase as the tilt-angle of the glazing changes from -30° to 30°. The east and the west fenestration are the main factor for DSHG in summer. Compared to them, the north has less gain and the less rate of increase. If the glazing system is tilted outward by 15° or 30°, there is no direct sunlight coming into the south fenestration so there is no peak for the orientation. But with vertical or some inward tilt, the south fenestration gets a great deal of direct sunlight and its change rate increases as the inward tilt angle increases. (-)30 tilt (-)15 tilt Vertical 15 tilt 30 tilt South 0 0 4.399363 20.1239591 38.86085619 West 17.8389302 28.01753835 36.59402643 44.94690654 51.38518523 North 5.832395396 7.253182481 8.179677165 10.12132887 14.73259256 East 26.59300081 35.01765141 44.97160549 51.6228281 58.24225586 0 10 20 30 40 50 60 70 BTU/ft^2 Summer Peak 51  Miami, Florida Figure 29: Total direct solar heat gain of glazing in different angle of tilt , Miami, FL Similar to the result from Phoenix, South, West and East fenestrations have a similar rate of increase if the surface is tilted, more but North has a different rate of addition. The other features are almost identical to Phoenix. Figure 30 is the same as Phoenix. The south fenestration is the best as it has much larger value than the other facades. The tendency of the difference between winter peak and summer peak has a similar pattern in the three other orientations. The main difference from Phoenix is that whereas -15° tilt has the larger difference than 15° tilt in the south in Phoenix, in Miami, 15° tilt has the higher ratio than the west. 52 Figure 30: Winter peak - summer peak, Miami, FL Figure 31: Summer DSHG peak, Miami, FL (-)30 tilt (-)15 tilt Vertical 15 tilt 30 tilt South 11.72406324 25.25618895 38.91489544 34.26896418 23.24160102 West -3.257798569 -7.431481379 -10.4993689 -15.66250892 -20.00210817 North -6.135753951 -7.415130541 -8.7281116 -11.29135056 -25.20375202 East -6.964346272 -10.2400403 -15.07701363 -17.42886821 -22.98103638 -30 -20 -10 0 10 20 30 40 50 Winter Peak - Summer Peak (BTU/ft^2) Winter Peak - Summer Peak (-)30 tilt (-)15 tilt Vertical 15 tilt 30 tilt South 0 0 1.19557E-05 12.99592761 38.86085619 West 18.99801164 29.7579294 37.31893047 45.37261562 52.72068489 North 6.135753951 7.415130541 8.7281116 11.29135056 25.20375202 East 26.70493796 34.98338982 44.38399083 51.6228281 57.21983711 0 10 20 30 40 50 60 70 BTU/ft^2 Summer Peak 53 All of the patterns and behaviors are same as Phoenix. The only difference lies on the south fenestration. The change rate is much bigger in Miami when the inward-tilt angle increases.  Minneapolis, Minnesota Figure 32: Total direct solar heat gain of glazing in different angle of tilt in Minneapo lis, MN Figure 32 shows the total direct solar heat gain in Minneapolis. Unlike Phoenix and Miami, every fenestration has a linear pattern of increase if it is tilted from outward to inward. Even north glazing represents the same behavior as the others. 54 Figure 33: Winter peak - summer peak, Minneapolis, MN In contrast to Phoenix and Miami, -15° tilt is the most preferable angle for the south fenestration. If the south fenestration is tilted more than 30°, it has negetive value of winter peak minus summer peak, which is undesirable. The overall graphs are similar in the west and east but the north does not show much difference with variety of tilted angles. The west fenestration has a positive difference value between winter peak and summer peak with -30°, which means winter peak is larger than summer peak. (-)30 tilt (-)15 tilt Vertical 15 tilt 30 tilt South 52.9110324 63.31761815 43.84286323 23.5829783 -0.779380018 West 5.874881919 -6.267082953 -17.28810387 -31.12691769 -41.64040021 North -2.330556156 -3.997025443 -9.802007367 -11.66870514 -14.83205017 East 0.907804063 -12.00954161 -25.07357307 -35.9075425 -47.49518415 -60 -40 -20 0 20 40 60 80 Winter Peak - Summer Peak (BTU/ ft^2) Winter peak - Summer Peak 55 Figure 34: Summer DSHG Peak, Minneapolis, MN Figure 34 shows the summer DSHG peak in Minneapolis. The biggest differences between Minneapolis and the hot climates are on the north and the south facades. Compared to the summer peak value for the north fenestration in Phoenix and Miami, the peak of the north is half: 2.33 BTU/ft 2 to 14.83BTU/ft 2 . The south fenestration gets a large amount of DSHG if it is tilted inward. Another difference lies is on the south; with a 15° outward tilt, it can still receive direct sunlight, which the hot climates do not get any with the angle of tilt. The west and the east fenestration dominate the summer peak values. (-)30 tilt (-)15 tilt Vertical 15 tilt 30 tilt South 0 6.929090856 37.26763924 62.04283087 73.43513266 West 29.90009223 48.38126999 61.31181964 74.27326748 83.01219173 North 2.330556156 3.997025443 9.802007367 11.66870514 14.83205017 East 36.05855209 53.65701406 70.07805134 79.70724376 90.35976322 0 10 20 30 40 50 60 70 80 90 100 BTU/ft^2 Summer Peak 56  New York, New York Figure 35: To tal direct solar heat gain of glazing in different angle of tilt, New York City, NY The tendency of the results is almost identical to Minneapolis. In Figure 36, all of the features are the same as Minneapolis except the south fenestration. For vertical glazing (with no tilt), the south has a similar value to -15° tilt whereas Minneapolis has much smaller value in vertical glazing than -15° tilt glazing. At 30° outward tilted glazing has the largest difference in all of three orientations: east, west and north. For the south façade, -15° tilt is the most desirable. South West North East (-)30 tilt 35258.04895 30860.79819 485.898966 32317.50967 (-)15 tilt 67745.6287 51726.63697 845.6483492 54008.15892 Vertical 110516.5873 73861.19686 1971.439099 76424.78772 15 tilt 153287.1396 95899.74568 3596.394439 98753.96025 30 tilt 185478.1343 116232.8126 12471.47366 118114.8909 0 50000 100000 150000 200000 (BTU/ft^2) Total Direct Solar Heat Gain (a year) 57 Figure 36: Winter Peak- summer Peak, New York City, NY Figure 37: Summer DSHG Peak in New York City, NY (-)30 tilt (-)15 tilt Vertical 15 tilt 30 tilt South 39.64563458 61.52899753 54.3299688 36.49076141 11.28448711 West 3.226128786 -7.331239652 -17.83682504 -28.7294213 -40.87843202 North -2.211757132 -3.771858727 -9.439708026 -11.37819059 -16.74338799 East -1.792546501 -13.84009576 -23.95038351 -34.94893897 -44.59527073 -60 -40 -20 0 20 40 60 80 Winter Peak - Summer Peak (BTU/ft^2) Winter Peak - Summer Peak (-)30 tilt (-)15 tilt Vertical 15 tilt 30 tilt South 0 1.23288E-05 20.51354112 46.37009427 73.43513266 West 32.97513922 50.67213275 64.13952062 77.15649418 87.7907079 North 2.211757132 3.771858727 9.439708026 11.37819059 16.74338799 East 33.04425668 52.02203737 65.74015229 79.70724376 89.27190703 0 10 20 30 40 50 60 70 80 90 100 BTU/ft^2 Summer Peak 58 All of the patterns and behaviors are the same as Minneapolis, but only a small difference in that the east and the west has almost identical summer peak value regardless of the angle of tilt or the direction of tilt (inward or outward). From this observation one can tell that in New York City, the east and west fenestration behaves similar and independent from angle of tilt. The only difference lies on the time when the peak occurs. In conclusion, all of the facades receive more direct solar heat gain if it is tilted inward and less for the outward tilt. With consideration to the DSHG behavior in winter and summer peak pattern, one can conclude that the greater outward tilt is good for the east and the west fenestration. At the same time, an outward tilt for the north façade also can be of merit if we consider reducing the heating load in winter. For the south, it is better not to tilt the glazing very much inward as this leads to a worse performance in both in winter and summer: less difference of winter peak and summer peak and high peak value in summer. If one focuses more on summer peak value than the winter contrast ratio, the east and west fenestration should have an outward tilt as these two orientations dominate the direct solar heat gain over the summer. For Miami, inward-tilt for the north is negative, and the outward-tilt in Minneapolis is definitely preferable. In general, outward tilt is beneficial, but too much inwards-tilt is negative for all of the orientations. As discussed in this chapter, DSHG behaviors and their effect on heating/cooling load are quite different based on the angle of tilt and orientation. Therefore, ASHRAE should take into account these tilt effects when they set up the SHGC requirements for glazing systems. Otherwise, the expected energy performance of the building would never be 59 achieved or could even cause wrong design decisions to be made by architects. It is obvious that considering the angular dependence of direct solar heat gain prescriptively would be complicated and might cause chaos. However, it is time to improve the energy code so that it can adapt to more complex geometry of buildings, especially since this condition is becoming more common. 60 Chapter 4 Case Studies Some buildings have tilted glazing not only for aesthetic reasons, but also as an environmental response. Three case studies will be discussed. These projects examine the application of tilted glazing as a strategy for energy efficient building. 4. . 61 4.1. Tilted Glazing in Contemporary Building Projects As previous chapters have discussed, some architects design high-rise buildings with complex geometries that are in strong contrast to the box-shaped buildings of the past. Although they often cost more than standard buildings, architects continue to design innovative high-rise buildings. As the public acceptance of these buildings improves, they are more willing to pay more for the design because they appreciate the aesthetic value. The emergence of tilted glazing initially attracted attention based on the striking appearances of buildings with complex shapes, but currently, some building professionals use complex forms for energy-efficient design strategies. The unusually exaggerated shapes of the building often come with tilted glazing. The inclined transparent surfaces behave differently depending on the location, orientation and angle of tilt, as already discussed in Chapter 3. The energy performance of the entire building may be different, depending on the different shapes of mass and façade geometries. Three case study projects are introduced in this chapter: Ropemaker Place, Tencent Head-quarters, and the International Finance Center in Seoul. 4.2. Ropemaker Place, London, UK Ropemaker Place is a commercial building near Moorgate in the City of London, United Kingdom. It is a BREEAM “Excellent” rated projec t and was designed by Arup Associates. This project is a great sustainable design using tilted glazing strategies while still incorporating flexibility needed in modern office buildings. 62 4.2.1. Building Information Figure 38: West façade, Ropemaker Place, London EC2, The Arup Journal, 2010 The Ropemaker’s façade design demonstrates the integration of design and engineering. The façade system uses tilted geometry so that the system itself can play a role for the shading. The angle and direction of tilt is varied depending on the orientation of each façade. The glazing system assemblies act as the integrated solar shading, as the windows “turn their backs” to the sun and thereby reduce solar gain and consequent cooling loads just like vertical fins. According to building physics report of Arup, the tilted façade system helped to reduce cooling load of the building up to 27 percent compared to the vertical glazing system (with no tilt). The facade is not excessively glazed and the windows are rotated away from the sun – east-and-west facing windows are rotated towards the north around a vertical axis, while the south-facing windows are rotated around a horizontal axis, leaning forward. The rotation means that an element of self shading is achieved 63 similar to what would have been achieved by means of fins and overhangs (Figure 39) (The Arup Journal 2010). Figure 39: Conceptual idea of tilted glazing, Ropemaker Place, London EC2, The Arup Journal, 2010 A second order effect is the reduction in solar transmission of the glazing for extended periods of time due to the resulting increase in the solar angle of incidence. The bay window design inevitably leads to an increase in thermal transmittance due to the greater developed transmission area and, more importantly, the bay window framing leading to some degree of linear and point thermal losses (The Arup Journal 2010). As this façade system contains unusual geometry, the detail of the system is critical. Arup provides a successful detail that includes excellent thermal breaks. The façade system is intended to be prefabricated (Figure 40). The adjacent details show both the east and west and the south elevation conditions and what impact these different orientations will have on the proposed collar details which allow the glass to be sloped relative to the unitized frame. The intent here is to provide a sufficiently well thermally broken collar to enable the average U-value figure of 2.0W/m²K to be achievable (Arup Building Phy sics Report 2006) 64 Figure 40: Adjacent details, Ropemaker Place, Building Physics Report – Stage C Rev 02, 2006 The Ropemaker Place is one of the best case study projects for tilted glazing as a sustainable design strategy. The façade system cleverly utilizes the angular dependence of direct solar heat gain for the south and the east/west. Although the design can be considered quite simple and repetitive, it is undoubtedly a milestone for tilted glazing strategies. 4.2.2. Flat Façade and Tilted Façade Comparison based on the Spreadsheet In Rhino, typical units for the south and the east/west of Ropemaker Place were re- modeled to extract accurate angles of tilt and the area of each surface (Figure 41). 65 Figure 41: Rhino 3d model with tilted surfaces Arup pointed out that they could have reduced cooling load up to 27% with the tilted glazing system. As summer peak DSHG is directly related to the cooling load calculation, the summer peak results from the master spreadsheet were analyzed (Figure 42 and 43). Based on the spreadsheet result, it is seen that the east has only 4.5% DSHG peak reduction but the south shows 20.0% and 10.9% reduction. One can tell the south façade takes a major role for the entire cooling load reduction with tilted effect, and the west also has good reduction rate. In contrast to these two fenestration studies, the east has minimal reduction. In general, all of the tilted glazing has less summer peak DSHG than the vertical glazing under same surface area. The resulting reduction percentage is different from Arup’s result. The spreadsheet calculation was only applied to one glazing system unit, whereas Arup’s result came from the cooling load of the whole building simulation. The input climate condition, especially the direct solar radiation values, might be also different. The tilted glazing does reduce the cooling load; further study would be needed to directly compare these results. 66 Figure 42: Rhino 3d model with spreadsheet calculation: vertical glazing and tilted glazing Figure 43: DSHG Comparison: vertical glazing and tilted glazing East South West Vertical 2940.683085 2375.096509 2845.495213 Tilted 2807.819947 1899.034792 2535.970837 0 500 1000 1500 2000 2500 3000 3500 BTU Summer Peak DSHG 67 4.3. Tencent Seafront Headquarters in Shenzhen, China Figure 44: Tencent Seafront Headquarters: perspective and tilted glazing, Courtesy of NBBJ Tencent Seafront Headquarters also used tilted glazing to improve the energy efficiency of the building. This section shows the performance analysis of the tilted glazing, which is done by Atelier Ten, to improve the existing façade design. Figure 45 shows the analysis on the south façade’s shading performance for the original design also demonstrating the preliminary shading reduction target (Atelier Ten 2010). The shading effect of the original façade design, which is done by NBBJ, shows the possible reduction of incident solar radiation up to 30 percent with 1.5 meters of projected plate (Figure 45). However, their shading reduction target is 45 to 50 percent which is a lot more than the possible effect from the original design. Based on the Atelier Ten’s analysis, even though 68 they can make a significant EUI improvement, still, the façade system needs additional shading consideration. Figure 45: Tilted glazing as shading device, 5672 Tencent South Facade Shading Memo, Atelier Ten, 2010 Figure 46 shows the alternatives of the original façade system to improve the energy performance. The 45-50% south façade shading reduction target was determined through a shading sensitivity test on a blank south façade with a simple horizontal shade tested at cut-off angles of 10° increments (Atelier Ten 2010). Based on the report of Atelier Ten, the shading reduction begins to diminish significantly at 45-50% shading. 69 Reduction was achieved with a 50° cut-off angle (Figure 45). This target is a preliminary design guideline that will be tested in greater detail in the Design Development energy model, to be prepared by Atelier Ten (Atelier Ten 2010). Figure 46: Optimal angle studies, Tencent Headquarters Final Book, 2010 In this study, Ecotect was used to determine the % reduction in radiation received, but not the absolute number for radiation received on the surface. This used the incident solar radiation also called solar exposure tool in Ecotect. The initial move to tilt the glazing down or toward the north was to reduce solar heat gain. The percentage reduction in the incident solar radiation (radiation received on the surface) was calculated seasonally, then input into the energy model in eQUEST. The energy model includes direct solar heat gain in its analysis. As the process shows, Atelier Ten used Ecotect for initial-simple study for tilted glazing. This study accounted for solely incident solar radiation but not for direct solar heat gain. As already discussed in Chapter 3, the incident solar radiation study cannot replace the 70 direct solar heat gain calculation. Because the direct solar heat gain calculation includes the angular dependence of incident solar radiation and glazing properties itself. Instead, eQUEST was used to make the energy model includes direct solar heat gain in its analysis. 4.4. International Finance Center, Seoul, South Korea The International Finance Center (IFC) buildings are a prime example of mixed-use construction projects. The project consists of office towers, a mall, and a hotel. Currently, the IFC is working toward LEED Silver certification from the U.S. Green Building Council, The total floor area is 3,529, 876 square feet. This project’s buildings are faceted. Tower A was chosen to be explored with the spreadsheet calculation, in Chapter 3. Figure 47: International Finance Center (IFC): under construction, WHK 71 4.4.1. Building Information Tower A consists of 29 stories and a penthouse (Figure 48). Of its eight faceted surfaces, four of them are tilted at different angles: 4.59°, -3.36°, 12.88°, and -3.85°. The surface areas are all different with 18044 ft 2 , 5554.4 ft 2 , 17090 ft 2 , and 12972 ft 2 . The orientations of the tilted surfaces are almost directly east and west, as they are 277° and 97°. Figure 48: IFC Plan: Ground floor and the second floor, Construction drawings, Courtesy of GS E&C Corporation Figure 49 IFC Elevation: Ground floor and the second floor, Construction drawings, Co urtesy of GS E&C Corporation 72 Figure 50: Glazing properties, KCC Glass Data, Courtesy of GS E&C Corporation Figure 51: Glazing properties: office tower vision, KCC Glass Data, Courtesy of GS E&C Corporation Based on this geometrical information and these glazing properties (Figure 50 and 51), the spreadsheet calculation was conducted to see the extent to which DSHG is different in flat and tilted glazing. 73 4.4.2. Flat Façade and Tilted Façade Comparison based on the Spreadsheet In Rhino, Tower A was re-modeled to extract accurate angles of tilt and the area of each surface (Figure 52). Figure 52: Rhino 3D model with tilted surfaces Figure 53 and 54 show the comparison between the flat surfaces. From the spreadsheet result, it is seen that Surface 2 and Surface 4 are tilted outward, having less DSHG; however, the difference is relatively- minimal. In contrast, Surface 3 has a large DSHG difference, as it receives more sunlight due to the inward tilt toward the west orientation (97°). An interesting aspect is shown in Surface 1: a small degree of inward tilt allows the surface to receive less DSHG, whereas most of the inward tilt glazing has more solar gain than the vertical (flat) fenestration. This phenomenon is related to the speed of the movement of the sun and the rotation of the earth. In certain location and certain angle of tilts, reversed results can sometimes be obtained. 74 Figure 53: Rhino 3D model with spreadsheet calculation: vertical glazing and tilted glazing Figure 54: DSHG Comparison: vertical glazing and tilted glazing Surface1 Surface2 Surface3 Surface4 Total Vertical Glazing 6037901.324 1858618.882 2904274.6 2204461.68 13005256.49 Tilted Glazing 5892957.793 1849065.314 3880985.19 2165390.016 13788398.31 0 2000000 4000000 6000000 8000000 10000000 12000000 14000000 16000000 DSHG (BTU) DSHG Comparison between Vertical and Tilted Glazing 75 As this study shows, examples of faceted building design have different DSHG performance. It is important to consider the different orientation and angles of tilt, as inward tilt does not always necessarily provide the building with more heat gain. In other words, the tilted angle, the surface azimuth, and the site location influence on DSHG interplay in such a way that there is no exact tendency or easy way to consider the angular dependence. Therefore, this angle-dependence of DSHG needs to be carefully taken into account for the energy codes and building energy simulations. Architects need to have a thorough knowledge of tilted glazing and its energy performance-related issues when designing a building with complex geometry. As reviewed in this chapter, some of the contemporary buildings have tilted glazing and faceted geometry and their DSHG behaviors are certainly different from the vertical (with no tilt) glazing. Some of the projects used the tilt effect for sustainable design strategy as a certain tilt angle for the specific location and orientation did show possible DSHG reduction. Tilting the glazing is not simple as it usually comes with more exposed surface area and it causes extra heat loss/gain through the glazing materials. Therefore, architects should design the component for façade systems more thoroughly and the façade detail of the Ropemaker Place shows this aspect well. All in all, architects need to understand the feature of DSHG with tilt effect to design façade or building more sustainable. 76 Chapter 5 Building Energy Simulation Programs One critical concern in this research paper is the realization that glazing might be tilted on a building façade. Several building simulation programs (Ecotect, eQUEST, IES and EnergyPro) were investigated to check if inclined glazing had been properly accounted for. In the review, two issues are considered: if the program itself either imports or calculates the SHGC at a different angle of incidence for each glazing system, and if the complex façade geometry can be modeled accurately in the programs. 5. . 77 5.1. Ecotect Ecotect was reviewed to see if it accurately takes into account tilted glazing and DSHG through the glazing. Autodesk® Ecotect® Analysis, sustainable design analysis software, is a comprehensive concept-to-detail sustainable building design tool (Ecotect website). It is popularly used for the initial study in sustainable design. Ecotect Analysis deals with several aspects of building performance: whole-building energy analysis, thermal performance, water usage and cost evaluation, solar radiation, daylighting, and shadows and reflections. Compared to other building energy simulation software programs, Ecotect is easier to use, as the interface is similar to those of Auto CAD and Rhino, both of which are frequently used in architectural design. It also has the capability to import 3D models from different programs, such as Revit. In terms of angular dependence of glazing systems, Ecotect does not have the capability to import the Window5 files that provide accurate SHGC at different incident angles. There is only one section in which one can input the refractive index of glass, admittance, and SHGC, which is the value at the normal incidence. Ecotect uses the shading coefficient method, which is first calculated for standard, 1/8-in thick clear glass, then multiplied by the shading coefficient. Because this method uses the angular dependence of solar transmission and absorption for standard glass rather than the actual angular dependence, it can lead to errors in energy performance prediction. Ecotect does account for the tilted effect of glazing, but it is difficult to make a ‘correct model.’ In other words, the program assigns surface normal to wall and window and then ignores any surface which points away from the sun. But this is invisible when inputting 78 and rendering the model. This sometimes results in inaccuracies, especially in imported surfaces and occasionally with surfaces drawn within Ecotect, since the surface normal is determined by the clockwise or counterclockwise order of the polygon points. Figure 55 shows the possible inaccuracy that can occurs in the modeling of tilted glazing. There are two sets of tilted glass surfaces. Even though they have exactly the same angles of tilt and size, the amount of incident solar radiation on the surfaces are different, as shown by the color variation (note that the dark blue color represents less incident solar radiation). The first set has various colors, which means that the received solar radiation on each surface is different from the others. However, the second set has the same colors, even though the two surfaces have different angles of tilt. As this figure clearly shows, the program does not consider these two sets as to be similar. The normal face in opposite directions but users can easily assume that they are the same because they look exactly the same in the 3D modeling screen. Under the Basic Data feature, Ecotect provides all of the information of the selected object, such as orientation, size, and so on. From this feature, Ecotect recognized the glazed objects in the first set as south-facing but the glazed objects in the second set as north-facing. The reason why Ecotect recognized these two sets differently is that the order of surface construction is different. 79 Figure 55: Modeling tilted glazing in Ecotect When the user wants to construct a south-facing surface based on vertices, the vertices should be assigned in a counter-clock wise direction. Otherwise, entering vertices in clockwise order creates the opposite surface normal, so it would be recognized as a north-facing surface. This difference is the reason why their incident solar radiation results are not identical. This case indicates that it is easy to build an incorrect geometry in Ecotect, leading architects to make erroneous decisions when they apply the performance results from Ecotect to their schematic design phase (Figure56). Figure 56: Modeling a complex façade in Ecotect 80 5.2. eQUEST eQUEST uses DOE-2.2, as its calculation engine and consists of a shell that writes files that are read by DOE in sequence, in order to perform the calculations (Milne, 2010). It contains complex simulations of building systems and occupancy schedules. It can model the interaction between loads, systems, plants, and economics. The program is extensively used in the building industry. eQUEST can import a Window5 report as the optical properties of the specific glazing system. Use of these windows improves the accuracy of the calculations, because the windows represent actual products and the simulations employ the angular properties of the glazing systems from Window5 (James J. Hirsch & Associates, 2006). However there are three ways to determine window optical properties in eQUEST with DOE-2.2: window shading coefficient method, window library method, and window layers method (DOE-2.2 Document, 2006). A user who chooses the first method enters the window’s shading coefficient, visible transmittance, and conductance. The second method requires that the user simply chooses the window from the window library in eQUEST. Importing the Window5 report is the third method. To obtain an accurate calculation based on the angular dependence of the specific glazing systems, this third method is the best choice, as glazing systems can have coatings or multiple layers that may confound the program’s ability to produce an accurate calculation. In the 3D modeling screen, eQUEST has the capability to accept the tilt of wall at user specified angles, which can then assigned the same tilt to the window, as well. 81 Figure 57 shows the definition of tilt in a diagram used here. The angle of 0° defines vertical glazing with no tilt, and the other angles are expressed as tilting toward the outside or inside (Figure 57). Figure 57: Tilt angle definition diagram Figures 58, 59, and 60 show the difference among spreadsheet results based on the ASHRAE Fundamentals Handbook calculation and the eQUEST solar gain value at the peak time of each month. Spreadsheet calculations are always less than the eQUEST value, but the configurations are similar to each other, with the exception of the 75 degree inward tilt in springtime. There is a high rate of change for the spreadsheet calculation, but a smooth changing rate in eQUEST. These differences might be a result of weather data difference or the ground reflection. 82 Figure 58: Solar gain in vertical glazing Figure 59: Solar gain in 15 degree inward tilt glazing Figure 60: Solar gain in 15 degree outward tilt glazing 0 10 20 30 40 50 60 70 1 2 3 4 5 6 7 8 9 10 11 12 105-equest 105-spreadhseet 83 In Figure 60, the largest difference of the 105 degree glazing, 15 degree outward tilts is shown. From the spreadsheet result, there is no DSHG during June to July, but eQUEST does show some of the gain in that summer period. It seems that eQUEST also accounts for ground reflection in the DSHG calculation. 5.3. IES/VE Integrated Environmental Solutions (IES) VE-Pro is one of the popular building energy simulation programs among the building energy consultants. It has the capability of importing Revit and SketchUp files, and it can even be connected as a plug-in toolbar for these architectural modeling programs. It provides detailed HVAC input options for users and includes the capability of modeling a complex building geometry. Heat gain calculation in VE is carried out for one design day in each of a user-selected range of months, using weather data provided in APlocate (Apache Calc User Guide). In glazing properties, a direct Window5 report import is not currently available within the VE but the calculated results from the Window5 tab for transmittance, reflectance and emissivity can be hard-entered in to the Glazed Construction tab (Waddell and Kaserekar 2010). Based on these inputs, VE automatically provides derived parameters (Figure 61). 84 Figure 61: Glazing properties in IES-VE The derived properties of glazing are given using an analysis based on the Fresnel equations. Figure 62, 63 and 64 show the comparisons between spreadsheet and VE results. Similar to the eQUEST, VE also takes account for ground-reflected gain in to the solar gain calculation. However, the calculation was conducted based on only the design day so this might be the reason why they have similar configuration but a bit different values. As previously mentioned, VE has the capability of modeling tilted surface or glazing accurately using the vertices -oriented method in ModelIT under the surface-edit tab. The one difference from Ecotect is that in VE, the user needs to input the specific distance for at least two vertices at the same time to tilt the wall if the wall already has a window. In addition, the user needs to change the window parameters. This is in another menu where he/she can say the angle of wall that a window is set in. The minimum tilt angle needs to be set to 0 so that it will be able to place into the wall user edited before for the angle. 85 Figure 62: Solar gain in vertical glazing Figure 63: Solar gain in 15 degree inward tilt glazing 86 Figure 64: Solar gain in 15 degree o utward tilt glazing 5.4. EnergyPro EnergyPro is a certified program under California Code Compliance (Title 24). The non- residential version uses the DOE-2.1e engine. Even though it is not intended as a design tool, EnergyPro does have performance reports for Title 24 or LEED compliance, and thus many building professionals use this program. Compared to other programs, this one lacks many input options for detailed modeling and does not have a 3D modeling screen. The user simply inputs all the numbers that define the geometry of the building, but the actual 3D building geometry is not shown. If incorrect numerical data is entered, the user would not easily realize that the modeling result is also incorrect. In addition, the most problematic issues concern the input variation for different orientations and the lack of input for the tilt of walls and windows. There are only four sections for wall orientations, assigning orthogonal to each other. This assumption is an issue of concern if the user has a faceted building with more than four orientations for walls and windows. At the same time, there is no input for the tilt angles of walls and 0 10 20 30 40 50 60 70 80 JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 105-spreadhseet 105-ve 87 windows, so users are forced to comply to the vertical wall only. As this paper previously pointed out, the tilt angle for window greatly affects the DSHG. If the user assumes that the all the windows are vertical rather than tilted, then the projected total energy performance of the building should vastly differ from the actual building performance. In terms of the effective SHGC of each glazing system, EnergyPro has only one input for solar heat gain calculation, which is SHGC at normal incidence. They have a window library, but it simply provides the SHGC value. It is clear that EnergyPro’s window library is not at all comprehensive, as the list of glazing systems is very simple (Figure 65). The user can add customized glazing properties but inputs are limited by SHGC at normal incidence; there is no input section for the accurate angle-dependence. Figure 65: Modeling tilted glazing in EnergyPro In terms of the effective SHGC of each glazing system, EnergyPro has only one input for solar heat gain calculation, which is SHGC at normal incidence. They have a window 88 library, but it simply provides the SHGC value. It is clear that EnergyPro’s window library is not at all comprehensive, as the list of glazing systems is very simple (Figure 65). 5.5. Integration between Energy Calculation and Schematic Design Phase As reviewed in this chapter, energy simulation programs either do not have any or enough capability to take the complex geometry of tilted glazing of buildings into account, as the DSHG for those buildings is a critical part of the building energy performance prediction. Also, the process of the energy calculation in simulation programs is quite different from design tools such as Rhino. Therefore, in the next chapter, a possible way to integrate DSHG (a main factor in determining cooling loads) and faceted building design (with tilted glazing) will be introduced. This integration is specifically based on the generative algorithm in Grasshopper, using the raw data from the spreadsheet calculation and conducting real-time iteration studies. 89 Chapter 6 Form-Refinement Process based on a Parametric Tool This section introduces an algorithm developed in Grasshopper (a plug-in for Rhino 3D), linking to the master spreadsheet. This algorithm can extract the surface azimuth and tilt angle of any surface from a given faceted form of a building in Rhino, and the surface information is input back into the spreadsheet to calculate the DSHG of the surface. Based on this process, one can easily calculate the total DSHG of a whole building. 6. . 90 6.1. Introduction Advances in technology have been improving the building design process. One of the important capabilities of building professionals is controlling the tremendous amount of data and information that is now associated with buildings. Intelligent software programs allow architects to study design parameters in digital phase, and some of the programs even have to suggest design solutions for architects. The ability to use the appropriate software programs and integrated them with design intuition has become one of the most important criteria for a technology-savy architect. There is still a huge gap between building energy performance prediction and sustainable building design. Many architects would like to apply sustainable design strategies in the early design process, but current energy simulation programs may not have sufficient capability to do so in a meaningful way. Many building simulation programs are not user-friendly, and sometimes the energy calculating process is not flexible enough to apply it directly in the schematic design phase. This makes it more difficult to integrate building performance simulation within the design process even when sustainable design is the goal. In addition, to make better decisions, architects may need the iterative studies of their design, but their energy simulation program may not have features to make this easy to accomplish. This chapter describes an extensible parametric design tool for assessing the performance of tilted glazing systems in faceted buildings. A Grasshopper parametric definition was used for integrating early design phase studies with one of the building energy performance criteria, DSHG. Based on the hand calculation result from the 91 master spreadsheet, a potential way to integrate building energy simulations and form- refinement processes of faceted buildings in schematic design phase was introduced. This algorithm can serve to be one of the functions of future building simulation programs that can be more intuitive and user-friendly, thus affecting the overall building shape design with regard to the efficient use of DSHG. In order to show the possible contribution of the form-refinement process, a faceted building design was studied (Figure 66). The use of the parametric tools allows not only for accurate results, but also almost instant variation of direct solar heat gain performance when each of the surfaces has different angle and orientation. The complexity of this study lies in real-time linkage of the spreadsheet calculation and geometry iteration, which resulted in DSHG data exchange within various forms of the faceted building. The form-refining process was designed by using Rhino as a modeling tool, Grasshopper as a parametric interface, the spreadsheet for DSHG evaluation, and Galapagos for problem solving. 92 Figure 66: A case project; a faceted building design Rhino (http://www.rhino3d.com) is a 3d NURB-based modeling program. Until relatively recently, it has not been easily used in conjunction with simulation software. Grasshopper® is one of the parametric tools used by the architectural design industry (Davison, 2009). It is becoming popular with both architecture students and building professionals. Grasshopper is used not only for architectural design, but also for building engineering and research. Grasshopper is a graphical algorithm editor tightly integrated with Rhino’s 3 -D modeling tools and can be used by designers who are exploring new shapes by employing generative algorithms. Unlike other parametric tools which require 93 that the user have previous programming knowledge, Grasshopper is relatively easy to use. The master spreadsheet used in this study includes the incident angle calculation based on the specific location, time, and surface azimuth. The effect of incident angle was reflected in direct solar heat calculation based on perpendicular direct incident sola r radiation and the effective SHGC to produce the spreadsheet. Using this spreadsheet, one can predict the amount of DSHG from each area of tilted glazing, with time- dependence throughout the year. Galapagos is a component of Grasshopper and it deals with problem-solving evolutionary systems based on the generative algorithm. 6.2. Galapagos; Genetic Algorithm in Grasshopper With the introduction of generative and parametric systems for architectural design, the number of iterations an architect can produce has become limitless. (Miller, 2010) However, as architects continue to negotiate complex design problems requiring iterations, variations, and alternatives, it becomes necessary to simultaneously formulate systems for evaluation and validation. Genetic algorithms and evolutionary systems provide a framework by which optimal (locally optimal) solutions can be searched for within an infinite generative field of variation. Using these tools, the parametric system becomes the genome, the field of alternatives becomes the population, and the architect’s design goal becomes the fitness criteria. 94 An examination of the evolutionary system shows that it uses principles of natural selection to automate the search for optimal solutions. One can use evolutionary system s to look for design solutions that meet certain criteria. Following steps are the brief overview of how it works: (Miller, 2010)  Step1. Created the initial population: The algorithm creates a random list of chromosomes and chromosomes with better traits have better fitness  Step2. The algorithm sorts the population based on fitness  Step3. Create some offspring: The algorithm combines traits from parents to produce children  Step4. Continue creating generations: Repeat the evaluation and breeding process Figure 67: Galapagos, an evo lutionary component in Grasshopper (See Appendix A) Evolutionary computing for the purposes of optimization can be conducted for a different number of objectives. The following figures show the difference between single- objective and multi-objective optimization algorithms in Grasshopper (Figure68 and 69). 95 Figure 68: Single-Objective: Galapagos was used to optimize a parametric model using o ne fitness goal. Figure 69: Multi-Objective: Galapagos was used to optimize a parametric model using two or more fitness goals. 6.3. Conceptual Idea In this research thesis, this evolutionary component was used for the form -refinement process of a faceted building. Without visual editing software such as Grasshopper, this process would have been possible only with time-consuming calculations and multiple iterations in the past. At the present time, technical innovation allows such studies to be conducted in an easy, quick and accurate way. This algorithm was developed further in Grasshopper to demonstrate form refinement of faceted building facades with an emphasis on the angle-dependent DSHG of glazing, a key factor for determining cooling 96 and heating load. The intent is to provide a visual tool where architects could fine tune their initial ideas for the massing of a building and help them determine a better angle of glazing for the building and its overall geometry in a specific climate zone. Figure 70 shows how the form-refinement process is conducted with Grasshopper and the spreadsheet. As a starting point, a faceted building model in Rhino was created. This algorithm can extract the surface azimuth and tilt angle of any surface from a given faceted form of a building in Rhino. The surface information is input back into the spreadsheet to calculate the DSHG of the surface and then the calculated DSHG value from the spreadsheet will be extracted and exported to the Galapagos solver. The solver would determine if the value is part of an optimal solution under the design constraints of Galapagos (such as minimum or maximum value) or not. This algorithm acts as a feed-back loop so architects can have iteration studies without manually inputting options in the simulation programs every single time. Figure 70: Grasshopper linked to spreadsheet 97 6.4. Design Tool Documentation This section documents the proposed design algorithm that can be used to determine an optimized configuration for the faceted building for better DSHG performance. The algorithm is applied to a case project composed of 70 faceted surfaces. The definition utilizes the master spreadsheet as the calculation engine for DSHG. The definition has been divided into screenshots that are shown in this section. Each screenshot describes one part of the definition. Figure 71: Grasshopper definition structure (see Figure 87 as a supplemental file) Figure 72 shows the geometry construction process. The vertices of the faceted surfaces move along the assigned ellipse. The slider in Grasshopper represents the position of each vertex. If the value in the slider changes, the location of each vertex on the ellipse will consequently move. In addition, the surface that is created based on the three 98 vertices will also change. These changes will be directly applied to the geometry of the faceted building. Figure 72: Geometry construction process Each time that the slider value changes, an iteration will be conducted, and the Galapagos solver will find the best solution which meets the certain constraints that a user inputs. The vertices of the faceted surfaces move along the assigned ellipse. The slider in Grasshopper represents the position of each vertex (Figure 73). Figure 73: Sliders in Grasshopper and consequence geometry change 99 6.4.1. Base Tower Outline The basis of the design was originated from seven typical plans. There were two different ellipses for the boundary for plans; the smaller one represents the minimum boundary and the larger one is the maximum boundary. The first, the third, the fourth, and the seventh typical floor used the big ellipse as their floor boundary and the others were applied to the small ellipse. At first, two boundaries were assigned as “Ellipse” components to one of the definition shown in Figure 74, and were duplicated using “Move” components in Grasshopper. Prior to the ellipse duplication, the number of duplications and the offset distance input to a “Series” component (Figure 74). Then, the whole building outline is defined (Figure 75). Figure 74: Grasshopper definition: base tower outline 100 Figure 75: Base tower outline in Rhino 6.4.2. Faceted Surfaces Construction Using a “List Item” component, all of the duplicated ellipses can be retrieved from a list: “0 to 6” for “i” value in the component; each “List Item” component indicates each ellipse. Then, the “List Item” component was connected to five “Evaluate Curve” components to separate the ellipse into five sections. Each section was assigned one vertex and the vertex can move on the any location within the section. The slider value means that the location of the vertex ranges from 0 to 0.2, 0.2 to 0.4, 0.4 to 0.6, 0.6 to 0.8, and 0.8 to 1. (1.0 is the same as 0: the starting point and end point are same as the base curve is an ellipse) A “Polyline” component connects these five vertices and finally, it can be a configuration of the typical plan. 101 Figure 76: Grasshopper definition: vertices of each surface Through the resulted poly lines, a “Loft” component created a lofted surface and then it was deconstructed into faceted surfaces. In this process, several components were used: “Explode” to decompose the loft, “Divide Domain” to divide a loft -surface domain into equal segments, “Isotrim” to extract an isometric subset of each surface, and “4Point Surface” to create a surface connecting three vertices (Figure 77). Figure 77: Grasshopper definition: surface construction 102 6.4.3. Surface Azimuth and Tilt Angle Extraction This section of the definition has two different parts: Surface Azimuth Extraction and Tilt Angle of the Surface. Each surface was assigned with an “Evaluate Surface” component to set up the normal vector of the surface. The z-vector from “Plane components” was selected and input to the “Vector Decompose” component. Based on the resultant vector, other components such as “Reverse Vector” were used to calculate the surface azimuth and tilt angle of the surface. Figure 78: Grasshopper definition: surface-angle information extraction 6.4.4. Linking the Master Spreadsheet to Grasshopper Surface-Angle information that was obtained from the previous definition was input to an “Excel Write” component to send the information to the master spreadsheet which was introduced in Chapter 3. In Figure 79, two of the yellow green cells are input cells. If the Grasshopper definition grabs the surface information, the “Excel Write” component directly sends the data to the spreadsheet and the values to these input cells. Then, the 103 spreadsheet automatically calculates the DSHG throughout a year and the average value. After that, the “Excel Read” component reads the average DSHG value from the spreadsheet and sends the number to a “Galapagos” component (Figure 80). If the model changes, the spreadsheet result will automatically trigger and update within Grasshopper. Figure 79: Master spreadsheet input cell location Figure 80: Grasshopper definition: excel write and read 104 6.4.5. Galapagos; Form-Refining Process As a final step of definition, Galapagos was added to find a locally optimal solution given the input constraints by users. This algorithm acts as a feed-back loop so architects can have iteration studies without manually inputting numerous options in the simulation programs that may not even be the best solution. Figure 81: Grasshopper definition: Galapagos 6.5. Result and Observation By using the algorithm, a simple test with first ten floors (20 faceted surfaces) of the building was conducted to check how this system works. The building was located in Phoenix, Arizona and Minneapolis, Minnesota. 105 Figure 82: Resulted geometries Figure 82 shows the two resulting geometries of the building for two climates with different criteria: maximum DSHG and minimum DSHG. This form-refinement process is under certain design criteria, (in this case, the building geometry constraints) such as the vertices need to move along with the given ellipse, and there are five vertices on each ellipse. Therefore, this algorithm follows the architect’s design intention but at the same time, it gives her the better geometrical design decision by refining the overall shape and tilt of the faceted building. 106 Chapter 7 Conclusion This chapter provides a summary of the work in this thesis. In addition, the conclusion of the discussion based on the proposed algorithm and result comparisons and a possible method for further development is also included. 7. . 107 7.1. Summary and Conclusion Many architects have been pursuing innovative designs, spurred by technological advances that help turn building concepts into reality. The geometry of buildings or facades has become much more complex from the typical box-shape or simple-vertical design of the past. Along with the changes in design, energy issues have become more important than ever, as society experiences shortages in energy and confronts energy- related issues such as global warming. Sustainability is not really a new vocabulary for the field of architecture, but in many cases it has yet to be fully integrated into actual building design since its inception. At present, the building construction industry is increasingly pursuing high-performance buildings. However, existing codes and building energy simulation tools sometimes do not have the capability to account for the innovative design in terms of energy efficiency in architecture. One reason for this is that the codes and simulation programs were developed for typical shapes, generally rectangular. This lack of capability is especially critical with regard to fenestration of high-rise office buildings, which have a large proportion of glazed area. Therefore, this research pointed out the importance of improving the current energy code and energy software to deal with more complex façade designs. This research focused on the effect of angular dependence on direct solar heat gain (DSHG) from tilted glazing. Research on variables that affect the optical properties of inclined glazing has been done, and one of the main variables, angle of incidence, was specifically chosen to be investigated in this research. The prescriptive path in ASHRAE 90.1 defines requirements of glazing properties depending on climate and building type, regardless of the angular dependence of solar heat gain. For example, the current SHGC is independent of the angle of incidence. By presenting the comparative results from a 108 master spreadsheet that includes incident angle calculation based on the specific location, time and surface azimuth, this research verified that this independence leads to errors in predicting building performance. The effect of incident angle was reflected in direct solar heat calculation based on perpendicular direct incident solar radiation and the effective SHGC to produce the spreadsheet. Using this spreadsheet, the amount of DSHG from each area of tilted glazing can be predicted with time-dependence throughout the year. As the spreadsheet results in Chapter 3 clearly show, the angular dependence of direct solar heat gain can create large differences between the various angles, orientation and direction of the tilt. If ASHRAE does not consider these effects on the prescribed building envelope requirements, it would generate serious errors when architects and building engineers design a building to meet the energy performance or simulate the whole building energy criteria. The analysis presented in Chapter 3 makes use of the numeric comparisons based on the spreadsheet calculation. Based on the comparison, all of the facades receive more direct solar heat gain if it is tilted inward rather than outward. In some cases, inward or outward tilting makes this contrast much more prominent. Therefore, ASHRAE should take the tilt effect into effect when setting up the SHGC requirements for glazing systems. Otherwise, the expected energy performane of the building cannot be achieved. This research alsoreviewed building energy simulation programs with regard to the angular dependence of DSHG, and a possible integration between genetic algorithm and a schematic design process. Some of the building simulation programs can apply the accurate angular dependence of DHGC of tilted glazing, but some of them do not recognize the effect in these complex geometries. These discrepancies are not only due to some lack of capability of building energy simulation programs to take into account tilted 109 glazing, but also because of 3d modeling issues. A user can easily create a model in the simulation program using different geometrical values, but it could be difficult to recognize if it is correct or not for that specific software program’s calculations; even if surfaces look the same, they may not be equivalent. Rhino, Grasshopper, Galapagos were used to demonstrate one possible method of combining design and energy simulation. The algorithm acts as a feedback loop in Grasshopper based on the accurate DSHG values calculated from a master spreadsheet. With this, architects can perform iteration studies without manually inputting options in the simulation programs every single time. One of the difficulties in applying energy simulation results to the design decision is that the user cannot easily carry out parametric studies. The algorithm can yield results in real-time iteration studies, while being faster, more user-friendly, and perhaps more intuitive. These characteristics affect the overall building shape design in relation to the efficient use of DSHG. 7.2. Future Study Two major developments could be the next steps in this study: improving the Grasshopper algorithm in detail and researching the various aspect of tilted glazing other than DSHG.  Multi-objective Galapagos Solution The algorithm introduced in Chapter 6 focused only on the DSHG aspect to find out the refined-form for specific building designs. This approach has several limitations. Because energy simulations have to consider many other issues, including HVAC 110 systems, schedules, properties of materials such U-value, etc. However, the approach demonstrated in Chapter 6 is a first step towards integrating schematic design and energy simulation programs. Future work could focus on the additional layers to the algorithm considering the complex climate conditions and enhance the user-specified constraints such as geometrical conditions or shaded effect from adjacent buildings. One issue regarding the maximum and minimum amounts should be addressed due to its complexity. DSHG can be added or subtracted based on energy consumption for cooling or heating. For example, the climates of certain places, such as Denver, CO, have relatively hot outdoor temperatures over the summer months, whereas the dry-bulb temperature of the city needs heating from November to March. In cases like these, DSHG should be minimized only for the summer months and maximized for the winter months (Figure 83). Figure 83: Overall concept of building balance point 111 A multi-objective Galapagos study can be conducted with the balance point temperature concept of weighting methods. The balance point is the outdoor air temperature, causing building heat gains to be dissipated at a rate that creates a desired indoor air temperature. For the multi-objective study, a weighting system should also be developed with different values for each month.  Application of Grasshopper Algorithm to a Unitized Façade System Design Given the area for a unitized façade system, parametric studies to determine the optimal geometry or angle of tilt for glazing can be conducted using the Grasshopper algorithm introduced in Chapter 6. The user can utilize the number of vertices for a unit. The algorithm can then determine the optimal height of the vertex with the angular dependence of DSHG and the heat gain/loss based on the total area and the U-value of the glazing. The concept is illustrated in Figure 84. Figure 84: Conceptual sketches: a unitized façade system with tilted glazing 112  Angle-dependence of DSHG in Coated glazing with Tilted Geometry Another possible further direction of this research would be how coated glazing performs at oblique angles of incidence as it cannot be calculated by current equations but it only can be obtained by experiment with calorimeter. It would be interesting that testing the coated glazing and analyze the results with different types of coatings such as solar control, low-e, and antireflection.  Relationship between DSHG from Tilted Glazing and Urban Context This research limited its scope to a single building but in reality, the surrounding urban context including the neighboring buildings needs to be taken into account particularly if the building is located in a high-density area. The neighboring buildings can provide shade or block the appropriate amount of daylight seeping into a space. Therefore, adding one more layer to the Grasshopper Definition or researching more about the relationship between tilted glazing and the surrounding conditions would be a critical direction to pursue in the future. 113 BIBLIOGRAPHY A.K. Designs LLC DBA Accent Windows 2008, Types of glass, Accent Windows, accessed October 2011, <http://accentwindow.com/faq.html>. American Society of Heating Refrigerating and Air-Conditioning Engineers 2005, The 2005 ASHRAE Handbook—Fundamentals, ASHRAE Research, p.31.4-31.41 Arasteh, D., Kohler C. 2009. Modeling Windows in Energy Plus with Simple Performance Indices. Atelier Ten 2010, 5672 Tencent South Facade Shading Memo, Courtesy of Atelier Ten. Atelier Ten 2010, Tencent Seafront Headquarters Final Book, Courtesy of Atelier Ten. Autodesk, Inc. 2012, Autodesk Ecotect Analysis, Autodesk, accessed March 2012, <http://usa.autodesk.com/adsk/servlet/pc/index?id=12602821&siteID=123112>. Davison, S. 2012, About Grasshopper…, Grasshopper-Generative Modeling for Rhino, accessed November 2011, < http://www.grasshopper3d.com/>. Deal B., Nemeth R, DeBaille, L., 1998, Energy Conservation Strategies: Windows and Glazed Surfaces, USACERL Technical Report 98/74, p.14-29. Ferguson, S. 2011, email 26 September, <sferguson@ashrae.org>. Integrated Environmental Solutions Limited, Apache Calc User Guide-IES Virtual Environment 6.3, accessed March 2012, <http://www.iesve.com/downloads/ help/ve64 /Thermal/ApacheCalc.pdf>. James J. Hirsch & Assiciates 2006, eQUEST version 3.6 and DOE-2.2 version 44 Released, accessed March 2012, <http://doe2.com/download/equest/ eQUEST3-6_DOE22-44_ReleaseFeatures.pdf>. James J. Hirsch & Associates and Lawrence Berkeley National Laboratory, DOE-2 Documentation, Basics, V.2.2, October 2004. Volume 1. Karlsson J., Roos A., 2000, ‘Modeling the angular behavior of the total solar energy transmittance of windows’ , Solar Energy, Volume 69, Issue 4, p. 321–329. Karlsson, J. 2001, ‘Windows-Optical Performance and Energy Efficiency’, PhD thesis, Uppsala University, accessed 15 September 2010 from Proquest Digital Thesis Database, p. 7-24. McLaren, W. 2009, US Buildings Account for 40% of Energy and Materials Use, Treehugger accessed 17 September 2010, <http://www.treehugger.com/sustainable-product-design/us-buildings-account- for-40-of-energy-and-materials-use.html>. 114 Miller, N. 2011, Introduction: USC Arch 517 Galapagos Course, The proving ground, accessed March 2012, < http://nmillerarch.blogspot.com/>. Milne, M. 2010, Advance Research in Environmental controls: Building Energy Performance Simulation, USC Arch 615 Course Document. Minasi, M. 2011, Equation of Time Calculator, Home of Technology Writer and Speaker Mark Minasi, accessed November 2011, < http://www.minasi.com/doeot.htm> . Olgyay, V. 1963, Design with Climate, Princeton University Press, p.26-31 . Olympus America Inc. 2011, Polarization of Light, Microscopy Research center, accessed October 2011, <http://www.olympusmicro.com/primer/lightandcolor/ polarization.html>. Regents of the University of Minnesota, Twin Cities Campus, College of Design, Center for Sustainable Building Research 2011, Issues in Window Selection: Energy- Related, Windows for high-performance commercial buildings, accessed November 2011, <http://www.commercialwindows.umn.edu/index.php>. Waddell, C., Kaserekar, S., 2010,“Solar Gain and Cooling Load Comparison Using Energy Modeling Software”, Proceedings of Building S imulation, 2010, New York. Wikipedia Foundation, Inc. 2011, Fresnel equations, accessed October 2011, <http://en.wikipedia.org/wiki/Fresnel_equations>. Windows and Daylighting Group, Building Technology Department, LBNL, Standards for Solar Optical Properties of Specular Materials, Window Optics, accessed November 2011, <http://windowoptics.lbl.gov/data/standards/solar>. Young H., Freedman R., 2007, University Physics, Pearson-Addison Wesley, p.1121- 1268. 115 APPENDIX: Galapagos (http://www.grasshopper3d.com/profiles/blogs/evolutionary -principles) Figure 85: Galapagos, an evo lutionary component in Grasshopper How does it work? – Detailed Description. 1. Galapagos populates the first generation (G[0]) with random individuals. Basically the sliders are all set at random values. 2. Now we step into the generic evolutionary loop, so G[0] becomes G[n], as this is the same for all generations. 3. For each individual in G[n] the fitness is computed. This is the most time consuming operation in the solver. 4. The individuals in G[n] must populate G[n+1], there are two ways in which this can happen: - Individuals 'survive' the generation gap and are present in both G[n] and G[n+1] - Individuals mate to produce offspring that populates G[n+1] Often, fit individuals will use both vectors. 5. Creating offspring is a complex procedure and there are many factors that affect it. a. Coupling: this step involves picking individuals from G[n] for mating couples. Individuals can be picked (i.e. everyone has an equal chance of being picked, regardless of fitness), exclusively (i.e. only the fittest X% are allowed to mate, but they are all 116 equally likely to mate) and biased (i.e. the fitter an individual, the higher the chance it finds a mate, but everybody has a chance) b. Mate selection: this step involves someone picking a mate from G[n]. When an individual has been selected to mate (step 5a), he/she needs to find a mate. Instead of picking another fit individual, mate selection happens based on genetic distance. For example, individuals could be said to prefer very similar individuals, or they could be said to prefer very different individuals, or something in between. This is called the "Inbreeding factor" in Galapagos. A high inbreeding factor will result in 'incestuous' couples, a low factor will result in 'zoophilic' couples. Neither extreme is healthy. c. Coalescence: Once a couple has been formed, offspring needs to be generated. Basically coalescence defines how the genomes of mommy and daddy are combined to produce little johnny. The best analogy with biological coalescence is crossover, where P out of Q genes are inherited from mom and (Q - P) genes are inherited from dad. In Galapagos, these genes are always consecutive, thus if the genome consists of 5 genes, the first 3 come from mom and the last 2 come from dad. Or the first 1 comes from mom and the last 4 come from dad. The amount of genes per parent is random. Genes can also be interpolated (there is no analogy for this in biological evolution). Since a single gene in Galapagos is nothing more than a slider position, it is quite easy to average the positions for mom and dad. Finally, genes can be created via preference blending. Very similar to interpolation, but the blending is weighted by the relative fitness of both parents. d. Mutations: Once the offspring genome has been created in step 5c, mutations are applied. Mutations are random events that affect gene values in random ways. Although the Galapagos engine supports several kinds of mutations, in Grasshopper it only makes sense to allow for point mutations, as it it not possible grow or shrink the number of sliders. 6. Finally, a new generation is populated and solved for fitness. There is an optional final step which can ensure that fit individuals do not get lost in the process. The "Maintain High Fitness" value controls what percentage of individuals from G[n] are allowed to displace individuals in G[n+1] provided they are fitter. By default this percentage is 10. Which basically means that the 10% fittest individuals in G[n] are compared to the 10% lamest individuals in G[n+1] and if grandpa is indeed fitter, he's allowed to bump junior off the list. 7. This process (step 2 - step 6) repeats until the maximum number of generations has been reached, until no progress has been made for a specified number of generations or until a specific fitness value has been reached.

Abstract (if available)

Abstract Contemporary cities are in a transition phase from primarily planar surfaces to a more dynamic urban fabric. One of the main contributors to this change is the development of shaped high-rise buildings that are in strong contrast to box-shapes of the past. This tendency makes accurate building energy simulation more difficult. Although sophisticated software exists to predict the performance of buildings and help architects and engineers make better decisions that reduce energy use, such programs are generally not able to deal with complexities of unconventional façade design. This is especially critical in regard to fenestration of high-rise office buildings, which have a large proportion of glazed area. Therefore, it has become important to improve the ability of energy software to deal with more complex façade designs. ❧ This research thesis focused on the effect of angular dependence on direct solar heat gain (DSHG) from tilted glazing. Variables that affect the optical properties of inclined glazing have been researched. One of the main variables, angle of incidence was chosen to be investigated in this research. The prescriptive path in ASHRAE 90.1 (ASHRAE STANDARD: Energy Standard for Buildings Except Low-Rise Residential Buildings) defines requirements of glazing properties depending on climate and building type regardless of the angular dependence of DSHG. For example, current SHGC is independent of angle of incidence. This can lead to errors in the building performance prediction. To improve DSHG calculation, a master spreadsheet that includes incident angle calculation based on the specific location, time and surface azimuth was developed. The effect of incident angle was reflected in DSHG calculation based on perpendicular direct incident solar radiation and the effective SHGC to produce the spreadsheet. Using this spreadsheet, one can predict the amount of DSHG through each area of tilted glazing, with time-dependence throughout the year. ❧ Next, an algorithm was developed in Grasshopper (a plug-in for Rhino 3D), linking to the master spreadsheet. This algorithm can extract the surface azimuth and tilt angle of any surface from a given faceted form of building in Rhino, and the surface information is input back into the spreadsheet to calculate the DSHG of the surface. Based on this process, one can easily see the total DSHG of a whole building. By using the algorithm, the DSHG values of a simple box-shaped building and a building with tilted geometry were obtained. The difference between the DSHG values clearly shows the importance of accounting for the angular dependence of glazing, which is not generally included in building simulation programs, energy codes, and even architects’ perceptions. Without visual editing software such as Grasshopper, this process would have been possible only with time-consuming calculations and multiple iterations in the past. At the present time, technical innovation allows such studies to be conducted in an easy, quick and accurate way. This algorithm was developed further in Grasshopper to demonstrate form refinement of faceted building facades with an emphasis on the angle-dependent DSHG of glazing, a key factor for determining cooling and heating load. The intent is to provide a visual tool where architects could fine tune their initial ideas for the massing of a building and help them determine a better angle of glazing for the building and its overall geometry in a specific climate zone.

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Asset Metadata

Creator Ko, Won Hee (author)

Core Title Tilted glazing: angle-dependence of direct solar heat gain and form-refining of complex facades

School School of Architecture

Degree Master of Building Science

Degree Program Building Science

Publication Date 05/15/2012

Defense Date 04/02/2012

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

Tag angle-dependence,direct solar heat gain,facades,form-refining,glazing,grasshopper,OAI-PMH Harvest,tilted

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Schiler, Marc (committee chair), Kensek, Karen M. (committee member), Simmonds, Peter (committee member)

Creator Email wonheeko@usc.edu,wonyko@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-40201

Unique identifier UC11288756

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Legacy Identifier etd-KoWonHee-850.pdf

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Rights Ko, Won Hee

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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 a...

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