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Effective light shelf and form finding: development of a light shelf design assistant tool using parametric methods

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Effective light shelf and form finding: development of a light shelf design assistant tool using parametric methods

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EFFECTIVE LIGHT SHELF AND FORM FINDING:

DEVELOPMENT OF A LIGHT SHELF DESIGN ASSISTANT TOOL
USING PARAMETRIC METHODS

By

Yue Liu

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

August 2013

Copyright 2013 Yue Liu

ii

Acknowledgements
I would like to express my gratitude to Professor Douglas Noble, the committee chair of my
thesis, for his guidance and encouragement during the whole process to help me developing an
understanding of the subject. Also I would like to show my deep gratitude to committee
members, Professor Marc Schiler, Professor Kyle Konis. They always share their knowledge
with me selflessly, encourage me from my perspectives and guide me with their valuable
suggestions to the right direction. Without the help from them, this thesis would not be possible.
I am thankful to Ilaria Mazzoleni and Jeff Landreth, who shared their knowledge on data analysis
with me and helped me to organize my data. Thanks to the design team members from AC
Martin and Glumac, Los Angeles, whose work inspired me to develop this thesis topic.
I must express my gratitude to school of Architecture, USC, who offered me the opportunity to
study and awarded me the scholarship to sponsor my study.
Thanks to Professor Karen Kensek and Professor Joon-Ho Choi, who guided me on lots of
research projects and gave me valuable advices on my future study and career development.
Thanks to all the faculties in Master of Building Science Program and my fellow MBS students
to accompany me during the 2 years of study like a big family. I learnt a lot from each of you and
will never forget the days we spent together in our MBS corner on second level of Watt Hall.
Finally, I have to express my deepest hanks to my parents and families members. Without their
encouragement and support, it would be impossible for me to complete my dream of studying
abroad.

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Table of Contents

Acknowledgements ............................................................................................................. ii
List of Tables ................................................................................................................... viii
List of Figures ..................................................................................................................... x
List of Equations ............................................................................................................. xvii
Abstract .......................................................................................................................... xviii
Keywords: ...................................................................................................................... xviii
Chapter 1 Introduction ........................................................................................................ 1
1.1 Background ........................................................................................................................... 2
1.2 Research Problem ................................................................................................................. 9
1.3 Hypothesis........................................................................................................................... 11
1.4 Objectives ........................................................................................................................... 12
1.5 Scope and Limitations......................................................................................................... 13
Chapter 2 Literature Review ............................................................................................. 14
2.1. Related Research Overview ............................................................................................... 15
2.2. Performance Indicators ...................................................................................................... 17
2.2.1 Daylight Factor ............................................................................................................ 18
2.2.2 Daylight Autonomy ..................................................................................................... 18
2.2.3 Daylight Autonomy Improvement ............................................................................... 19
2.2.4 Discussion and Comparison ......................................................................................... 19
2.3. Variables Affecting Light Shelf Performance ................................................................... 24
2.3.1 Light Shelves Mounting Position................................................................................. 25
2.3.2 Light Shelf Configurations .......................................................................................... 26

iv

2.3.3 Building Orientations and Location ............................................................................. 30
2.3.4 Materials ...................................................................................................................... 31
2.3.5 Ceiling Effects ............................................................................................................. 33
2.4. Daylighting Design Assistant Tool .................................................................................... 34
2.5 Summary ............................................................................................................................. 36
Chapter 3 Methodology .................................................................................................... 37
3.1 Groundwork ........................................................................................................................ 38
3.2 Software Preparation ........................................................................................................... 39
3.2.1 Daylight Simulation Software Investigation ................................................................ 39
3.2.2 Radiance Settings ......................................................................................................... 43
3.2.3 Grasshopper ................................................................................................................. 46
3.2.4 Galapagos; Genetic Algorithm in Grasshopper ........................................................... 47
3.2.5 Linking Results to Excel .............................................................................................. 48
3.3 Simulation Conditions ........................................................................................................ 48
3.3.1 Location ....................................................................................................................... 48
3.3.2 Design of Office Module and Test Points.................................................................... 49
3.3.3 Schedule ....................................................................................................................... 51
3.4 Research variables .............................................................................................................. 51
3.4.1 Independent variables .................................................................................................. 53
3.4.2 Dependent variables ..................................................................................................... 60

v

3.4.3 Constants ...................................................................................................................... 60
3.5 Design Tool Documentation ............................................................................................... 61
Chapter 4 Software Evaluation Problems and Suggestions .............................................. 67
4.1 Evaluation Methodology ..................................................................................................... 68
4.1.1 Test Modules ................................................................................................................ 68
4.1.2 Simulation Conditions ................................................................................................. 69
4.2. Potential Problems ............................................................................................................. 71
4.2.1 Material ........................................................................................................................ 71
4.2.2 Multiple Test Cells in One Simulation Model ............................................................. 75
4.2.3 Ground Plane Size and Test Module Position ............................................................. 78
Chapter 5 Daylighting Simulation Results and Analysis .................................................. 80
5.1 Preparation Tests and Data Analysis Methods ................................................................... 81
5.1.1 Room Depth Test ......................................................................................................... 81
5.1.2 Light Shelf and Overhang Shading Comparison Test ................................................. 82
5.1.3 Data Analysis Methods ................................................................................................ 84
5.1.4 Charts and Diagrams .................................................................................................... 85
5.2 35 feet Depth Room ............................................................................................................ 90
5.2.1 Light Shelf Height 7 feet.............................................................................................. 90
5.2.2 Light Shelf Height 8 feet.............................................................................................. 93
5.3 40 feet Depth Room ............................................................................................................ 96
5.3.1 Light Shelf Height 7 feet.............................................................................................. 96

vi

5.3.2 Light Shelf Height 8 feet.............................................................................................. 98
5.4 45 feet Depth Room .......................................................................................................... 101
5.4.1 Light Shelf Height 7 feet............................................................................................ 101
5.4.2 Light Shelf Height 8 feet............................................................................................ 103
5.5 50 feet Depth Room .......................................................................................................... 106
5.5.1 Light Shelf Height 7 feet............................................................................................ 106
5.5.2 Light Shelf Height 8 feet............................................................................................ 108
5.6 Light Shelf Variables Tendency Analysis ........................................................................ 111
5.6.1 Light Shelf Width Variable Analysis ......................................................................... 111
5.6.2 Light Shelf Curvature Variable Analysis ................................................................... 113
5.6.3 Light Shelf Tilt Angle Variable Analysis .................................................................. 115
5.6.4 Light Shelf Height Variable Analysis ........................................................................ 117
Chapter 6 Light Shelf Design Assistant Tools: Design Guideline and Quick Calculation
Equations......................................................................................................................... 119
6.1 Light Shelf Design Assistant Tools .................................................................................. 120
6.2 Light Shelf Design Guidelines .......................................................................................... 120
6.2.1 35’ Depth Room Light Shelf Design Guideline (baseline DA=45) .......................... 122
6.2.2 40’ Depth Room Light Shelf Design Guideline (baseline DA=25) .......................... 123
6.2.3 45’ Depth Room Light Shelf Design Guideline (baseline DA=7) ............................ 124
6.2.4 50’ Depth Room Light Shelf Design Guideline (baseline DA=0) ............................ 125
6.3 Quick Calculation Equations ............................................................................................ 126

vii

6.3.1. 35’Depth Room, 7’ Height Light Shelf .................................................................... 127
6.3.2. 35’Depth Room, 8’ Height Light Shelf .................................................................... 132
6.3.3. 40’Depth Room, 7’ Height Light Shelf .................................................................... 134
6.3.4. 40’Depth Room, 8’ Height Light Shelf .................................................................... 136
6.3.5. 45’Depth Room, 7’ Height Light Shelf .................................................................... 138
6.3.6. 45’Depth Room, 8’ Height Light Shelf .................................................................... 140
6.3.7. 50’Depth Room, 7’ Height Light Shelf .................................................................... 142
6.3.8. 50’Depth Room, 8’ Height Light Shelf .................................................................... 144
Chapter 7 Conclusion and Future Work ......................................................................... 146
7.1 Condition of the Study ...................................................................................................... 147
7.2 Tested Hypothesis ............................................................................................................. 147
7.3 Conclusion ........................................................................................................................ 148
7.4 Future Study ...................................................................................................................... 151
7.4.1 More Variables........................................................................................................... 152
7.4.2 More Performance Criteria ........................................................................................ 153
7.4.3 A Design Assistant Plugin for Rhino and Grasshopper ............................................. 154
Bibliography ................................................................................................................... 155

viii

List of Tables
Table 1: Comparison of Main Daylight Metrics .......................................................................... 23
Table 2: Comparison of four daylight simulation software of their model platform, engine and
indicator ........................................................................................................................................ 42
Table 3: Radiance Parameter and Description (Greg Ward Larson 2004) .................................. 43
Table 4: Radiance simulation parameters utilized in simulations................................................ 46
Table 5: Dependent and Independent Variables and Constants for Parametric Daylight
Simulation ..................................................................................................................................... 52
Table 6: Test Cases of Independent Variables ............................................................................. 53
Table 7: Floor, Wall, Ceiling and Ground Reflectance of Test Room ........................................ 61
Table 8: Light Shelf Upper Surface Radiance Material in This Study ........................................ 61
Table 9: Material Properties of the Test Module ......................................................................... 70
Table 10: Radiance Simulation Parameters ................................................................................. 70
Table 11: Light Shelf Combinations Rank for 35 feet Depth Room ........................................... 95
Table 12: Light Shelf Combination Rank for 40 feet Depth Room ........................................... 100
Table 13: Light Shelf Combination Rank for 45 feet Depth Room ........................................... 105
Table 14: Light Shelf Combination Rank for 50 feet Depth Room ........................................... 110
Table 15: Sample of Excel Spreadsheet to Conduct Regression Analysis ................................ 128
Table 16: Excel Regression Analysis Report: 35’ Depth Room and 7’ Height Light Shelf...... 129
Table 17: Excel Regression Analysis Report: 35’ Depth Room and 8’ Height Light Shelf...... 132
Table 18: Excel Regression Analysis Report: 40’ Depth Room and 7’ Height Light Shelf...... 134
Table 19: Excel Regression Analysis Report: 40’ Depth Room and 8’ Height Light Shelf...... 136
Table 20: Excel Regression Analysis Report: 45’ Depth Room and 7’ Height Light Shelf...... 138

ix

Table 21: Excel Regression Analysis Report: 45’ Depth Room and 8’ Height Light Shelf...... 140
Table 22: Excel Regression Analysis Report: 50’ Depth Room and 7’ Height Light Shelf...... 142
Table 23: Excel Regression Analysis Report: 50’ Depth Room and 8’ Height Light Shelf...... 144

x

List of Figures
Figure 1: Site Electricity Use in Office Building (198 billion kWh) (EIA 1995) ......................... 2
Figure 2: Basic Functional Concept of a Horizontal Light Shelf (Rungta 2011) .......................... 5
Figure 3: Different kinds of light shelves ...................................................................................... 6
Figure 4: Light shelf on HSBC’s Hong Kong Headquarter, and Atrium View (Bristolite
Daylighting Systems 2013) ............................................................................................................. 7
Figure 5: Photo and Section of SOKA-BAU Operable “Wing” (Herzog 2006) ........................... 8
Figure 6: Design Variables of Light Shelves and Rooms ............................................................ 10
Figure 7: The Resulting Daylight Factor Curves, Before and After the Addition of an Anidolic
System (Siân Kleindienst 2006).................................................................................................... 20
Figure 8: Internal (left), External (middle) and Combined Light Shelves (right) ....................... 25
Figure 9: Light Shelves Height Effect ........................................................................................ 26
Figure 10: Upward Tilted or Curved Light Shelves .................................................................... 26
Figure 11: The Two Chosen Tilted Angles for the Simulation Analysis of the Light Shelf and
Their Relations With the Angle of Obstruction (left two) The Curved Shape of the Light Shelf
(right 1) (Sabry 2006) ................................................................................................................... 27
Figure 12: Variable Area Light Reflecting Assembly (Howard 1986) ....................................... 28
Figure 13: Vertical Section Anidolic Zenithal Collector. A concentrator emerging from the
facade is designed to accept all incoming light from half the sky hemisphere. In the room, the
system comprises two reflectors that will "deconcentrate" the light flux and, therefore, shape it as
a beam of well-defined angular spread. Rays traced through the system (red lines) illustrate these
two properties. (EPFL 2013)......................................................................................................... 28
Figure 14: Anidolic System Configuration (Jean-Louis Scartezzini 2004) ................................. 30

xi

Figure 15: Light Shelves with Specular Finish (left) and Matte Finish (right) ........................... 32
Figure 16: Glare on Ceiling Caused by Glossy Reflection of Light Shelves .............................. 33
Figure 17: The Basic Consideration of Shaping the Ceiling Geometries and the Distance Used
to Shape Different Ceiling Geometries Based On the Light Reflected Light Shelf and Room
Height (A. Freewan 2008) ............................................................................................................ 34
Figure 18: Guidelines of Anidolic Light Shelf System Design (Siân Kleindienst 2006) ............ 35
Figure 19: Concept Workflow of This study ............................................................................... 39
Figure 20: Illuminance Level Calculation of a Living Room in Ecotect ..................................... 42
Figure 21: Two Ambient Bounces Numbers Have Very Different Results ................................ 44
Figure 22: Comparing Between Difference Ambient Bounce Setting of Their Daylight
Autonomy ..................................................................................................................................... 45
Figure 23: Light Shelf Shape Change under the Control of Grasshopper ................................... 47
Figure 24: Galapagos Is Trying to Find the Maximum Fitness Number ..................................... 48
Figure 25: Room Configuration and Sensors Location: Room Section (up), Room Plan (down)
....................................................................................................................................................... 49
Figure 26: Concept Diagrams Show Light Shelf Variables Comparisons .................................. 54
Figure 27: Diagram Shows Light Shelf Curvature (α) Definition .............................................. 55
Figure 28: Diagram Show Light Shelf Curvature and Tilt Angle Definition .............................. 56
Figure 29: New Light Shelf Configuration Definition for Future Study: Light Shelf is Tangent to
the Horizontal at the End Point ..................................................................................................... 57
Figure 30: Diagram Shows General Width (W) Definition of Horizontal Light Shelf ............... 58
Figure 31: Two Light Shelves with the Same Width................................................................... 58
Figure 32: Light Shelf Width New Definition for Future Study Reference: Effective Width .... 59

xii

Figure 33: Diagrams shows General Height (H) Definition of Horizontal Light Shelf .............. 60
Figure 34: Excel Write Components in Grasshopper .................................................................. 62
Figure 35: Variables Control Slider in Grasshopper ................................................................... 63
Figure 36: Variables Control Slider in Grasshopper ................................................................... 63
Figure 37: Galapagos Connects with Grasshopper Components ................................................. 64
Figure 38: Grasshopper Definition of Light Shelf Configuration ............................................... 64
Figure 39: the Grasshopper Definition of Sensor Points ............................................................. 65
Figure 40: DIVA Calculation Components in Grasshopper ........................................................ 65
Figure 41: Excel Write Components ........................................................................................... 66
Figure 42: Test Models: Test Room 1 without Any Shading (Above Left), Test Room 2 with 1”
Shading (Above Right), Test Room 3 with 8’ Shading (Middle Left), Test Room 4 with 100’
Shading (Middle Right), Test Room 5 with 8’ Light Shelf (Bottom) .......................................... 68
Figure 43: Simulation Settings in DIVA ..................................................................................... 71
Figure 44: DIVA Calculation Results of Test Room 1 without Any Shading ........................... 73
Figure 45: DIVA Calculation Results of Test Room 4 with 100’ Shading ................................. 73
Figure 46: DIVA Calculation Results of Test Room 4 with 100’ Shading ................................. 75
Figure 47: Change from Multiple Models in One Set to One Model Per Calculation ................ 76
Figure 48: DIVA Calculation Results of Test 1 with Five Models in one Simulation ................ 77
Figure 49: DIVA Calculation Results of Test 2 with Only One Model in the same place in one
Simulation ..................................................................................................................................... 77
Figure 50: Diagrams Shows the Change of Test Model Position according to the Ground Plane
in This Study ................................................................................................................................. 79
Figure 51: Diagram Shows the Change of the Ground Plane Size in This Study ....................... 79

xiii

Figure 52: Diagram Shows the Relationship between Room Depth and Daylight Autonomy
(DA) at rear of the room for room with and without light shelves ............................................... 81
Figure 53: Daylight Autonomy Distribution Diagram of the Rooms Using Four Different
Strategies: Without Light Shelf, With Overhang Shading, With Flat Horizontal Light Shelf, With
Curved Light Shelf ........................................................................................................................ 83
Figure 54: Sample Chart for Daylight Autonomy Analysis ........................................................ 86
Figure 55: Diagram Represent the Relationship between DA and Light Shelf Width ................ 87
Figure 56: Sample Chart of Light Shelf Variable Tendency Analysis ........................................ 89
Figure 57: Diagram Shows Relationship Between Light Shelf Variables (Curvature and Tilt
Angle) and Daylight Autonomy at 5 Feet from the Back Wall of the Room: 35 feet Depth Room,
7 Feet Height Light Shelf .............................................................................................................. 90
Figure 58: Diagram Shows Relationship between Light Shelf Variable (Width) and Daylight
Autonomy at 5 Feet from the Back Wall of the Test Room: 35 feet Depth Room, 7 Feet Height
Light Shelf .................................................................................................................................... 91
Figure 59: Diagram Shows Relationship Between Light Shelf Variables (Curvature and Tilt
Angle) and Daylight Autonomy at 5 Feet from the Back Wall of the Room: 35 feet Depth Room,
8 Feet Height Light Shelf .............................................................................................................. 93
Figure 60: Diagram Shows Relationship between Light Shelf Variable (Width) and Daylight
Autonomy at 5 Feet from the Back Wall of the Room: 35 feet Depth Room, 8 Feet Height Light
Shelf .............................................................................................................................................. 94
Figure 61: Diagram Shows Relationship Between Light Shelf Variables (Curvature and Tilt
Angle) and Daylight Autonomy at 5 Feet from the Back Wall of the Test Room: 40 feet Depth
Room, 7 Feet Height Light Shelf .................................................................................................. 96

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Figure 62: Diagram Shows Relationship between Light Shelf Variable (Width) and Daylight
Autonomy at 5 Feet from the Back Wall of the Test Room: 40 feet Depth Room, 7 Feet Height
Light Shelf .................................................................................................................................... 97
Figure 63: Diagram Shows Relationship Between Light Shelf Variables (Curvature and Tilt
Angle) and Daylight Autonomy at 5 Feet from the Back Wall of the Test Room: 40 feet Depth
Room, 8 Feet Height Light Shelf .................................................................................................. 98
Figure 64: Diagram Shows Relationship between Light Shelf Variable (Width) and Daylight
Autonomy at 5 Feet from the Back Wall of the Test Room: 40 feet Depth Room, 8 Feet Height
Light Shelf .................................................................................................................................... 99
Figure 65: Diagram Shows Relationship Between Light Shelf Variables (Curvature and Tilt
Angle) and Daylight Autonomy at 5 Feet from the Back Wall of the Test Room: 45 feet Depth
Room, 7 Feet Height Light Shelf ................................................................................................ 101
Figure 66: Diagram Shows Relationship between Light Shelf Variable (Width) and Daylight
Autonomy at 5 Feet from the Back Wall of the Test Room: 45 feet Depth Room, 7 Feet Height
Light Shelf .................................................................................................................................. 102
Figure 67: Diagram Shows Relationship Between Light Shelf Variables (Curvature and Tilt
Angle) and Daylight Autonomy at 5 Feet from the Back Wall of the Test Room: 45 feet Depth
Room, 8 Feet Height Light Shelf ................................................................................................ 103
Figure 68: Diagram Shows Relationship between Light Shelf Variable (Width) and Daylight
Autonomy at 5 Feet from the Back Wall of the Test Room: 45 feet Depth Room, 8 Feet Height
Light Shelf .................................................................................................................................. 104

xv

Figure 69: Diagram Shows Relationship Between Light Shelf Variables (Curvature and Tilt
Angle) and Daylight Autonomy at 5 Feet from the Back Wall of the Test Room: 50 feet Depth
Room, 7 Feet Height Light Shelf ................................................................................................ 106
Figure 70: Diagram Shows Relationship between Light Shelf Variable (Width) and Daylight
Autonomy at 5 Feet from the Back Wall of the Test Room: 50 feet Depth Room, 7 Feet Height
Light Shelf .................................................................................................................................. 107
Figure 71: Diagram Shows Relationship Between Light Shelf Variables (Curvature and Tilt
Angle) and Daylight Autonomy at 5 Feet from the Back Wall of the Test Room: 50 feet Depth
Room, 8 Feet Height Light Shelf ................................................................................................ 108
Figure 72: Diagram Shows Relationship between Light Shelf Variable (Width) and Daylight
Autonomy at 5 Feet from the Back Wall of the Test Room: 50 feet Depth Room, 8 Feet Height
Light Shelf .................................................................................................................................. 109
Figure 73: Visual Presentation of Light Shelf Width Variable in This Study ........................... 111
Figure 74: Performance Curve Represent Relationship between Light Shelf Width and DA at
rear of the room ........................................................................................................................... 111
Figure 75: Visual Presentation of Light Shelf Curvature Variable in This Study ..................... 113
Figure 76: Performance Curve Represent Relationship between Light Shelf Curvature and DA at
rear of the room ........................................................................................................................... 113
Figure 77: Visual Presentation of Light Shelf Tilt Angle Variable in This Study .................... 115
Figure 78: Performance Curve Represent Relationship between Light Shelf Tilt Angle and DA
at rear of the room ....................................................................................................................... 115
Figure 79: Visual Presentation of Light Shelf Height Variable in This Study .......................... 117

xvi

Figure 80: Performance Curve Represent Relationship between Light Shelf Height and DA at
rear of the room ........................................................................................................................... 117
Figure 81: Measured DA versus Predicted DA: 35’ Depth Room and 7’ Height Light Shelf .. 131
Figure 82: Measured DA versus Predicted DA: 35’ Depth Room and 8’ Height Light Shelf .. 133
Figure 83: Measured DA versus Predicted DA: 40’ Depth Room and 7’ Height Light Shelf .. 135
Figure 84: Measured DA versus Predicted DA: 40’ Depth Room and 8’ Height Light Shelf .. 137
Figure 85: Measured DA versus Predicted DA: 45’ Depth Room and 7’ Height Light Shelf .. 139
Figure 86: Measured DA versus Predicted DA: 45’ Depth Room and 8’ Height Light Shelf .. 141
Figure 87: Measured DA versus Predicted DA: 50’ Depth Room and 7’ Height Light Shelf .. 143
Figure 88: Measured DA versus Predicted DA: 50’ Depth Room and 8’ Height Light Shelf .. 145

xvii

List of Equations
Equation 1: Daylight Factor ........................................................................................................ 18
Equation 2: Sample Equation .................................................................................................... 127
Equation 3: DA Prediction for 35’ Depth Room with 7’ Height Light Shelf ........................... 131
Equation 4: DA Prediction for 35’ Depth Room with 8’ Height Light Shelf ........................... 133
Equation 5: DA Prediction for 40’ Depth Room with 7’ Height Light Shelf ........................... 135
Equation 6: DA Prediction for 40’ Depth Room with 8’ Height Light Shelf ........................... 137
Equation 7: DA Prediction for 45’ Depth Room with 7’ Height Light Shelf ........................... 139
Equation 8: DA Prediction for 45’ Depth Room with 8’ Height Light Shelf ........................... 141
Equation 9: DA Prediction for 50’ Depth Room with 7’ Height Light Shelf ........................... 143
Equation 10: DA Prediction for 50’ Depth Room with 8’ Height Light Shelf ......................... 145

xviii

Abstract
The transmission of sufficient daylight to offset electrical lighting, while maintaining
comfortable conditions for occupants, is the central objective for effective daylighting. Utilizing
a light shelf is a common strategy for enabling daylight transmission while controlling direct sun
and discomfort glare to maintain occupant comfort.
However, it is difficult for designers to optimize light shelf performance during design, as they
are required to choose from many different possible design configurations, each with multiple
variables (e.g. geometry, surface properties, and position within the facade). This study presents
a method for optimizing light shelf daylighting and visual comfort performance that utilizes Diva
for Rhino combined with parametric analysis and optimization to develop an integrated solution
based on multiple variables input by the user. The method is discussed in the context of results
from room simulations and façade optimization of a large commercial office building located in
downtown Los Angeles. The study concludes with recommendations for implementing this
method in the context of early-stage design decision-making to support energy reduction and
improved occupant comfort in commercial office buildings incorporating light shelves.
Keywords:

Light Shelf, DIVA, Radiance, Design Assistant Tool, Daylight Autonomy, Office Building

Chapter 1 Introduction

This research project focuses on optimizing light shelf daylighting performance in office
buildings. In this chapter, the importance of applying light shelves in office buildings as
well as the current problems and limitations of such applications are discussed; objectives
of the study are presented, along with insights into the methodology and intended
deliverable of this project.

2

1.1 Background
Daylighting plays an important role in architectural expression. Daylighting combines art
language and science language. Daylighting is a design element and also a part of the
environmental system. As a design element, daylighting could be used to enhance the
aesthetic performance of a space. As a science element, daylighting should also be
studied seriously in a qualitative and quantitative building science level.
There are many reasons for an architect’s preference of utilizing daylighting rather than
electrical lighting in an office building. Some of these reasons are: view, occupant
comfort, quality of light, energy saving, and the pure desire to have natural sunlight in
office space. Utilizing daylighting is a popular green strategy and can be used to obtain
credit from the LEED rating system.
In the United States, office buildings consume nearly 200 billion kWh of electricity every
year. (Moore, 1985) Of this, artificial lighting consumes 40%-60% of the total electricity
consumption (data of 1985 shows near 60% and 1995 shows 44 %). (Moore, 1985) (EIA
1995)

Figure 1: Site Electricity Use in Office Building (198 billion kWh) (EIA 1995)

3

The potential for energy saving by utilizing daylight as a light source is substantial. Also,
the use of daylighting could help to reduce cooling loads in summer that are generated
from the heat created by electrical light sources. A case study shows the energy savings
from reduced electric lighting through the use of daylighting strategies can directly
reduce building cooling energy usage by 10% to 20%. (Ander 2012)
A daylighting system is comprised not just of daylight apertures, but is coupled with a
daylight-responsive lighting control system. When there is adequate ambient lighting
provided from daylight alone, this system has the capability to reduce electric lighting
power. (Ander 2012) For economical consideration, utilizing free daylighting as a source
and saving electricity can save building owners significant amounts of money. For
example, according to a report provided by Gregg D. Ander, for many institutional and
commercial buildings, total energy costs can be reduced by as much as one-third through
the optimal integration of daylighting strategies. (Ander 2012) Moreover, utilizing
daylighting could also decrease electrical load during peak use time and peak pricing
time. Therefore, additional costs could be saved.
Researchers continue to work on studies regarding occupant productivity gains due to
daylighting. This is relatively complex and no clear results have been ensured, but to the
extent that this can be quantified, utilizing daylighting is likely to be attractive to owners
and occupants. (M. Susan Ubbelohde 2008) For example, according to a report done by
the Heschong Mahone Group, skylights were found to be positively and significantly
correlated to higher sales. All other things being equal, an average non-skylit store would

4

likely have 40% higher sales with the addition of skylights, with a probable range
between 31% and 49%. (Heschong Mahone Group 1999)

Daylighting is easy in many single story or low-rise offices because most occupants are
typically located near the building facade. However, daylighting is sometimes not easy to
achieve in multiple story or high-rise office buildings and providing daylighting can
become a design challenge to architects and consultants. Office design practice in the
United States tends to run counter to the architectural and technical requirements of
daylighting. Deep floor plates were preferred by owners and occupants for the
economical pursuit of low cost and easy to lease space. For this reason it can be difficult
to locate office workers within the easily day-lit perimeter zone of 15-20 feet. (M. Susan
Ubbelohde 2008)
It is difficult for most high-rise office buildings to achieve daylight by simply using
windows around the perimeter of the side lit building. Even when these side windows are
from wall to wall, this strategy can hardly supply sufficient sunlight deep into the space.
Therefore, only the small portion of those occupants located in area near the window can
benefit from the electrical saving by utilizing daylight.
Moreover, the contrast between the poor availability of daylighting in deep positions of
the space and the significantly high illuminance level near the window will affect light
uniformity and has the potential to cause glare discomfort for occupants when they look
at a dark face with excessive brightness from the window comes into their field of view.

5

(Abdulmohsen 1995) This uneven daylight distribution is common with side lit office
buildings. (Hopkinson 1966)
The general rule of thumb for side lit space is that daylight can penetrate two times the
height of window into the room. (Mistrick 1991)
Extra daylight strategies are needed for better utilizing daylight in office buildings, such
as increased daylight penetration and uniformity. Maintaining comfortable conditions for
occupants is the central objective for effective daylighting. Utilizing a light shelf is such a
strategy for enabling daylight transmission while controlling direct sun and discomfort
glare to maintain occupant comfort. Figure 2 offers a general concept for such a system.
Figure 3 gives a general idea of different kinds of light shelf systems.

Figure 2: Basic Functional Concept of a Horizontal Light Shelf (Rungta 2011)

6

Figure 3: Different kinds of light shelves

The light shelf is a classic daylighting system, known to the Egyptian pharaohs. It has
been used worldwide to improve interior lighting environments and help reduce energy
consumption. The HSBC’s Hong Kong Headquarters, which was designed by Sir
Norman Forster and built from 1979 to 1986, utilized one huge exterior light shelf on the
south facade above lower levels. This light shelf creates one strong horizontal line,
breaking the building into two parts. The lower surface of the light shelf is made of a
matte finish while the upper surface is composed of specular mirror panels, reflecting

7

sunshine to building’s atrium to light the lobby. Norman Foster created one beautiful and
bright open atrium that is rarely matched in other high rise buildings.

Figure 4: Light shelf on HSBC’s Hong Kong Headquarter, and Atrium View (Bristolite Daylighting
Systems 2013)

The extension to the head office of Soka-Bau, designed by Herzog and Partners is
another award-winning project utilizing interesting light shelves to help improve indoor
lighting and thermal comfort while reducing fossil energy consumption. The highly
developed building and engineering industry in Germany offer him the capacity to create
computer controlled operable light-deflecting “wing” on the south facade. When direct
sunlight hits the south facade, the wing moves to the shade position, and an assemblage
of concave louvers collect and redirect light in required quantities into deeper portion of
rooms. There is also a fixed panel to direct zenith-light.

8

Figure 5: Photo and Section of SOKA-BAU Operable “Wing” (Herzog 2006)

A light shelf can also be an effective daylighting system for office envelope retrofitting
projects. Some old office buildings haven’t been designed with daylight considerations.
In such cases, the window to wall ratio is limited because of construction limits and
aesthetic preference. Interior materials are sometimes darker which makes things even
worse. A light shelf is an easy solution. Installing a light weight light shelf has only
minimal requirements and effects on the building’s structure and existing envelope.
Industrialized light shelf products are manufactured by modularity, reducing the
installation time and cost. The retrofitting process happens primarily on the outside of a
building and will have minimal influence on the interior environment during installation.

9

1.2 Research Problem
One of the most significant benefits of using a light shelf is to improve the illuminance
value of areas deep in rooms by using redirected daylight. However, this goal is not
always achieved. Besides, Aizlewood observed that “any system for light redirection
must cause transmission losses,” which makes a light shelf system seem
counterproductive at first glance. (Siân Kleindienst 2006) Although a light shelf could
reflect a certain portion of sunshine in to rooms, which increases the illuminance value,
another portion of sunshine is blocked by the light shelf, which means less lumens of
light could enter the room and the total lumens in the room is reduced. A light shelf needs
to be carefully studied and designed to get a balance between the redistribution and
reduction.
Secondly, a light shelf is not always a simple horizontal slab. It could be made of
different kinds of shapes, sizes, materials, and mounted on different positions. Those
variables interact with each other to decide the performance of light shelves. The
performance of light shelves could also be influenced by windows, ceilings and room
configuration. (Figure 6) All those variables offer designers more choices to reinforce
their projects but also confuse them for picking the best product to meet their design
lighting requirements.

10

Figure 6: Design Variables of Light Shelves and Rooms

Thirdly, there is a gap between building performance predictions and sustainable building
design. To impact design decision making during the early stages of design, architects
require rapid feedback and interactive capabilities to explore various design strategies.
However, detailed indirect lighting calculation and study are time consuming, and it is
more time consuming to study all kinds of light shelf configurations. As a result, it is hard
for designers to make comparisons and make correct decisions for a specific case. In
addition, there is the ongoing matter of interoperability issues between design tools and
tools used for performance analysis. As a result, light shelves are usually judged
incorrectly in design and can lead towards improper directions.
There should be tools that can assistant architects and consultants to design an efficient
light shelf. The quantitative variables of light shelf should be analyzed together.

11

1.3 Hypothesis
The hypothesis of this study is that an optimum light shelf solution based on multiple
interconnected variables (light shelf depth, radius, height, tilted angle) applied to south
wall fenestration will achieve the objective of increasing light penetration into the interior
space.
The term “optimum” in this study is used to indicate that the light shelf solution which
provides the best daylight autonomy at rear of the room. This will be discussed later in
full detail in Chapter 3, Methodology.
The thesis is grounded in the context of results from room simulations and façade
optimization of a large commercial office building located in downtown Los Angeles.
The thesis concludes with recommendations for implementing this method in the context
of early-stage design decision-making to support improved occupant comfort in
commercial office buildings incorporating light shelves.
The final product will be a guideline or design assistant tool for architect and consultant
to design light shelf in a specific space.

12

1.4 Objectives
The objectives of this study are to achieve the following:
1. Determine the specific dependent and independent variables that appear in the
above hypothesis.
2. Demonstrate that the multiple variables that affect the performance of light
shelves are interacting with each other and need to be analyzed together.
3. Determine the appropriate indicator and criteria to evaluate light shelf daylight
performance.
4. Investigate current daylight simulation software of their application and
limitations and validate the software that be finally selected.
5. Develop a workflow that architects and consultants can use to determine the light
shelf daylight performance based on popular design software.
6. Compare building daylighting penetration of a case of South fenestration with the
optimum light shelf combination to a base case without a light shelf.
7. Determine the optimum light shelf that based on multiple variables of three
typical office rooms which facing south.
8. Develop a design assistant guideline or tool that help architects or consultant
design light shelves.

13

1.5 Scope and Limitations
The scope of this study is to analyze and evaluate the effect of utilizing a light shelf on
side windows to increase daylight penetration into the space. The study will develop a
method for optimizing light shelf daylighting and visual comfort performance and offer
integrated solutions based on multiple variables (e.g. height, width, radius, tilted angle).
However, the study will be limited to the following:
1. Only consider a fixed light shelf with no mechanical moving parts in the system.
This system is applied to the south-facing window of a building test module that
is located in Los Angeles (34°03′07″N 118°14′34″W)
2. The working schedule for the office building will be set to 8am to 6pm.
3. The south window will be a wall to wall window.
4. Only three typical room modules will be tested
5. The evaluation criteria will not include energy savings.
6. The light shelf included in this study will be mainly mounted exterior to the
window.

14

Chapter 2 Literature Review

This chapter introduces the background information of the research, includes an overview
of design factors and other studies related to this project, and also points out the issues
and limitations of the former studies.

15

2.1. Related Research Overview
A light shelf is generally a horizontal or nearly horizontal light-reflecting overhang
device positioned inside and/or outside of the window facade. It combines solar shading
and sunlight redirection. The high reflectance upper surface reflects sunlight up onto the
ceiling and redirects daylighting deeper into rooms; the solid overhang geometry blocks
direct sun in the area near the windows and reduce solar heat gain while reducing cooling
load in summer. It is an efficiency strategy that could help utilizing daylighting to
improve lighting quality in rooms with great depth, such as open offices, while reducing
lighting energy consumption during day time.
There are four key aims to light shelf design: “to increase daylight levels deep within
rooms, to improve daylight uniformity, to control direct sunlight and to reduce glare.” (P
J Littlefair 1994) Most of the previous research studies of light shelf focus on qualitative
and quantitative analysis and evaluation of light shelf performance. However, researchers
have not made a simple conclusion whether light shelves could work as they are expected
for several reasons.
First of all, researchers evaluate light shelf performance from different points of view,
which leads to the disagreement of light shelf efficiency. A light shelf could change the
lighting and thermal performance of a building and it is hard to find a balance to evaluate
between these two. What makes things more complex is that any perspective of these
could be evaluated in several different ways. For example, lighting could be evaluated
from lighting level, glare and uniformity views, and different indicators such as

16

illuminance value, daylight factor, and daylight autonomy and so on, aiming at evaluation
of different light shelf functions.
Secondly, a light shelf is not a single product but a huge family with members based on
several kinds of variables. To improve light shelf efficiency some researchers, such as
Claros and Linhart, have come up with several methods such as changing the reflectance
of the light shelf material. (Santiago-Toma's Claros 2001) (Friedrich Linhart 2010)
Freewan put the focus on design specific ceiling geometry to incorporate with the light
shelf thus makes it more efficient. (A. Freewan 2008) There are also a few researchers
such as Kim, Ga Young and Sabry, Hanan Mustafa Kamal who are exploring optimum
light shelf configurations by changing the variables such as angle and position of light
shelf. (Sabry 2006) (Kim 2009) So far, the anidolic light shelf system is one specific type
of light shelf that has been demonstrated to provide much better performance on
improvement of illuminance level than a flat horizontal light shelf. (Gilles Courret 1998)
However, it may cause some glare problems and needs to be used carefully. (Carlos
Ernesto Ochoa 2006) All those light shelf systems need to be carefully studied under
certain circumstances.
Even though light shelves are demonstrated to have the potential to perform well
according to previous research, there is little application of light shelves in real projects.
This is due to a lot of reasons, such as added cost, cleaning and maintenance difficulty,
clients and designer’s preference. Among them, clients and designers are not informed
about light shelf advantages is a possible reason. There are few research projects, such as
by Kleindienst and Linhart, focusing on the exploration of an assistant tool and guideline
on light shelf design. (Siân Kleindienst 2006) (Friedrich Linhart 2010)

17

Although these previous research projects examined light shelves and their performance,
further studies are needed to provide better quantitative information to support the design
of light shelves. The previous research and the limitations of them will be discussed in
detail later in this chapter.
This research study is focused on developing an assistant tool to help architects determine
appropriate geometry for light shelf to be utilized for daylighting purposes. The method is
discussed in the context of results from room simulations and façade optimization of a
large commercial office building located in downtown Los Angeles. Different types of
light shelves with different configurations (e.g. geometry, surface properties, position
within the facade) are simulated automatically in test rooms of different sizes to seek
optimized performance.
2.2. Performance Indicators
In the past two decades, there have been a number of explorations in daylight calculation
methods. The scientific daylighting studies started in 1895 with real measurement of
outdoor illuminance level. (Walsh 1951) Then some empirical methods and indicators
were developed to evaluate the performance of daylighting such as: Daylight Factor,
which right now researchers still use for daylight evaluation and Daylight Autonomy
which appeared recently and later some improvement of Daylight Autonomy such as
Useful Daylight Illuminance and Continuous Daylight Autonomy.

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2.2.1 Daylight Factor
Daylight Factor (DF) was first developed in the early 20th century, and can be defined
as the ratio of internal illuminance level to external illuminance level.
The equation below gives the further explanation of DF.

Equation 1: Daylight Factor
DF = (Ei / Ee) x 100%
Ei = illuminance level at a point on working plane inside the room,
Ee = simultaneous outdoor illuminance level at a point outside the room under overcast
sky condition.
2.2.2 Daylight Autonomy
Daylight Autonomy (DA) is one kind of "climate based metric", this is because it is
based on annual climate conditions and takes building location and orientation into
consideration. It can be defined as the percentage of daylight hours during a year that a
given test point is above some specified illuminance level. In late 20th century,
Association Suisse des Electriciens originally proposed the concept and was improved by
Christoph Reinhart during 2001-2004.

19

2.2.3 Daylight Autonomy Improvement
Continuous Daylight Autonomy (cDA) is based on Daylight Autonomy. It gives partial
credit to time steps when the illuminance level is lower than the DA requirement. For
example, if the threshold for DA to count is 400lux, during some specific time, the
illuminance level of one point is 200lux, DA will count 0, while cDA will count as 0.5
(400lux/200lux). (Reinhart 2006)

Useful Daylight Illuminance (UDI) is also based on Daylight Autonomy. UDI divides
the illuminance level into three parts, <100 lux, 100-2000 lux, >2000 lux. It will only
give credit to illuminance level between 100 lux and 2000 lux. (Reinhart 2006)

Daylight Saturation Percentage (DSP) is another modification of Daylight Autonomy
and based on UDI. It changes the UDI range from 100lux-2000lux to 40 foot-candles
(precisely 430 lux) to 400 foot-candles (4,300 lux). (Buildings 2013)

2.2.4 Discussion and Comparison
All performance indicators have their own advantages as well as disadvantages. (Table.
1) And because the limitations of these performance indicators, they can only be
appropriate used under certain conditions and assistant providing criteria to judge
different aspects of light shelf function.

20

The problem with illuminance level (lux) as the indicator is that it does not represent the
variation during different seasons and it is hard to combine the result into one number
and give the intuitive information for evaluation the performance of different light
shelves.
In 2006, Siân Kleindienst and Dr. Marilyne Andersen did a research project on
characterizing the effect of anidolic systems. (Siân Kleindienst 2006) Daylight Factor
was selected as the performance indicator in this research to test the increase in daylight
floor area. This is partly because the old version of LEED (Leadership in Energy and
Environmental Design) Green Building Rating System™ gives credit to buildings with
minimum of 2% daylight factor over 75% of the floor space. So the research also uses
this as criteria. (Figure. 7) The author mentioned in the future work part that more work
will be conducted with Daylight Autonomy rather than Daylight Factor.

Figure 7: The Resulting Daylight Factor Curves, Before and After the Addition of an Anidolic System
(Siân Kleindienst 2006)

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Daylight Factor (DF) is the most common metric of the daylighting study. But in spite the
popularity of Daylight Factor as an indicator in daylight performance presentation, it can
only be used under the overcast sky conditions. This makes it have serious limitations in
presenting daylight performance; first, it includes no account for sky luminance variation;
second, building orientation and location won’t affect the calculation results; glare
problem will not be informed because DF only account for direct daylight. The advantage
of the DF metric is that it will not take location, time and building orientation into
account (under overcast sky model), so it can be used to get quick and general
conclusions. It is a helpful and easy to use indicator to quickly compare the relative
daylight penetration when the climate includes mostly overcast sky and not good
indicator in climate with lots of sunlight.

Daylight Autonomy (DA) takes into account the direct daylight and based on year round
light condition simulation. It could present the effect of building orientation and location
on daylight performance. And researchers could set up the threshold to calculate the
percentage of time that room has sufficient daylight which makes electric lighting not
necessary. However, DA makes no account of the amount by which the threshold
illuminance was exceeded at any particular instant, which can inform about glare and
thermal discomfort.

22

Useful Daylight Illuminance (UDI) and Daylight Saturation Percentage (DSP) as
improvements based on Daylight Autonomy, it limits daylight calculation within a range.
As a result, it not only informs regarding the sufficiency of daylight but also the
possibility of excessive daylight that associated with glare problems, unwanted solar heat
gain and human discomfort. However, the threshold of UDI is 100 lux which is
somewhat lower than the amount of daylight people typically need in office buildings.
DSP is not an official indicator and has not been integrated into most of current
simulation software.
This thesis aims at evaluation two aspects of improvement after using a light shelf within
a room; light uniformity and availability of daylight. Besides, the author tries to seek a
simple way to present the results. So Daylight Autonomy was selected as the
performance indicator and two sensors were calculated to separately inform light
uniformity and availability of daylight.

23

Table 1: Comparison of Main Daylight Metrics
INDICATOR DEFINITION CONDITION

YEAR OF
FIRST USE
Daylight Factor(DF)
A Daylight Factor is
defined as the ratio of
internal illuminance level
to external illuminance
level.
DF = (Ei / Ee) x 100%
Ei = illuminance level at a
point on working plane
inside the room,
Ee = simultaneous
outdoor illuminance level
at a point outside the
room under overcast sky
condition.
DF can only be used under
overcast sky, it won't take
building orientation into
consideration because it
won't calculate direct sunlight
Early 20
th

century.
Daylight
Autonomy(DA)
Percentage of annual
daytime hours that a
given point in a space is
above a specified
illumination level.
DA is known as climate based
metric and can take location,
orientation into account. But
it makes no account of the
amount by which the
threshold illuminance was
exceeded at any particular
instant or not sufficient.
1989(first
raised)
2001-
2004(improv
ed )

24

Useful
Daylight Illuminance
(UDI)
Percentage of annual
daytime hours that a
given point in a space is
between 100 lux-2000 lux
Limit DA in 100lux-2000lux
range (However, no scientific
explanation for the range to
be defined as 100lux-2000lux)
2006
Continuous Daylight
Autonomy
(cDA)
Gives partial credit to
time steps when
illuminance level lower
than DA requirement

2006
Daylight Saturation
Percentage
(DSP)
Percentage of annual
daytime hours that a
given point in a space is
between 430 lux-4300 lux
DSP excludes the time when
electric lighting devices
needed and also exclude the
possibility of glare.
2006

2.3. Variables Affecting Light Shelf Performance
Because a light shelf can function to block the direct sun and help increase daylight levels
deep within a room, there is a need to find a balance between how much light to block at
the front of room and how much light to direct into the rear of room. To find such a
balance, variables that could affect light shelf performance need to be carefully analyzed.
Such variables included light shelf mounting height, geometry, building orientation,
location, material and the climate conditions.

25

2.3.1 Light Shelves Mounting Position
Light shelves could locate inside or outside or on both sides of a building facade. Internal
light shelf blocks less daylight, and it usually redirects less daylight into buildings. (Sabry
2006) External light shelves could redirect more daylight and work as overhang devices.
However, external light shelves are not able to block all direct sun light. Combined light
shelves could utilize the advantages of both and provide the most evenly distributed
illumination. (Abdulmohsen 1995) The inner part of light shelves could cause conflict
with fire sprinklers, which should draw special attention during design process.

Figure 8: Internal (left), External (middle) and Combined Light Shelves (right)

Light shelves often require high ceilings in a room. This is because a light shelf mounted
below eye-level will reflect sunshine directly to people’s eyes. (Figure 9) Lower light
shelf could also block people’s visual connection to exterior view, reduce ceiling height
visually and make people near window uncomfortable. A typical new construction high
rise building will have ceiling height of 9’ to 10’. This thesis tests 10’ ceiling only and
proposes that light shelves should be located in a range of 7’ to 8’ feet for the reasons
discussed above to make maximal use of daylight while not subjecting people to
disabling glare.

26

Figure 9: Light Shelves Height Effect

2.3.2 Light Shelf Configurations
Although light shelves are most well known as a simple horizontal slab, they are not
limited to this shape. Designers and researchers have done a lot of modifications based on
the idea of “redirect it deep into rooms”. For example, upward tilted or curved light
shelves have the potential to redirect sunlight deeper in to rooms.

Figure 10: Upward Tilted or Curved Light Shelves

27

Sabry in his research quantify the effect of the tilt angle and curved shape light shelf by
making two comparison cases: upward and downward tilt angle, curve versus flat. Figure
11, Figure 12) (Sabry 2006)

Figure 11: The Two Chosen Tilted Angles for the Simulation Analysis of the Light Shelf and Their
Relations With the Angle of Obstruction (left two) The Curved Shape of the Light Shelf (right 1) (Sabry
2006)

The results show the upward case and curved case could improve illuminance level at
rear of the room by nearly 30%. This research identifies some variables of light shelf
configuration that affect their efficiency and quantifies the individual effects of these
variables.
The limitation is the limited number of comparisons in the experiment which cannot lead
to a general guideline.
There are also some complex light shelf configurations. In 1986, Howard, T.C., W. Place
B. Anderson and P. Coutiers designed a patented product Variable-Area Light Reflecting
Assemblies (VALRA) as shown below, which use a reflective plastic film to redirect
sunshine in different angles.

28

Figure 12: Variable Area Light Reflecting Assembly (Howard 1986)

An anidolic light shelf is another complex system, which is believed to be one of the
most efficient light shelf systems. Anidolic stands for “non-imaging”, which makes use
of the geometric properties of parabolic curves to redirect daylight from all directions to
parallel lines aiming at the same direction and light deep into the room. (Figure 13)

Figure 13: Vertical Section Anidolic Zenithal Collector. A concentrator emerging from the facade is
designed to accept all incoming light from half the sky hemisphere. In the room, the system comprises two

29

reflectors that will "deconcentrate" the light flux and, therefore, shape it as a beam of well-defined angular
spread. Rays traced through the system (red lines) illustrate these two properties. (EPFL 2013)

There exist lots of research studies of this system. Gilles Courret proved an anidolic
system would improve human daylight comfort by real measurement and conducting
questionnaire investigation on occupant feeling. (Gilles Courret 1998) Scartezzini's
research shows that anidolic systems can improve the daylight factor at rear of the room.
(Jean-Louis Scartezzini 2004) Linharta's research shows that an anidolic system could
supply largely sufficient daylight during long periods on most working days. (Friedrich
Linharta 2009) However, anidolic systems may also cause some problems. In Ochoa's
research, three different systems that affect the penetration of daylight in a side lit office
space were analyzed: a single window without any external protection, a horizontal light
shelf and a basic anidolic concentrator, the systems are compared for illuminance and
glare performance. The result shows that the anidolic systems provide the highest
illuminance, but can have glare problems under certain conditions. While a light shelf
reduces the contrast level between levels at the view window and those at the back of the
room, it is sacrificing on illuminance levels. (Carlos Ernesto Ochoa 2006) An anidolic
system also takes too much space above the ceiling and usually causes conflicts with
other building systems. The curved exterior part also has a strong effect on building
aesthetics. As a result this system has not been widely used on building designs.

30

Figure 14: Anidolic System Configuration (Jean-Louis Scartezzini 2004)

Operable systems and anidolic systems need specific and complex designs which make it
difficult to define the variables. In order to simplify the research, only simple light shelf
systems will be discussed and these complex systems are not included in this thesis.
2.3.3 Building Orientations and Location
Building orientations and location are other factors that affect light shelf performance. To
make a light shelf function properly, it should be designed specifically for each climate,
latitude and window orientation.
Climate is a key question when considering light shelf applications. Light shelves may
not be suitable for all climates. They are not ideal in some tropical or desert climates with
intense solar heat gain where smaller openings are encouraged to reduce excess heat gain.

31

(Yaik-Wah Lim 2012) However, the efficient function of a light shelf requires direct
sunlight. In some cities such as London where the sky most of time is under overcast
condition, light shelves do not improve significantly the daylight levels. (Brotas,
Patametric Daylight Envelope: shading for maximum performance 2012) A horizontal
flat light shelf performs less well to block direct sunlight in high-latitude area and
additional shading will be needed during most time of the year. (LBNL 2000)
Light shelf efficiency strongly depends not only on the latitude but also on a building’s
orientation. A light shelf works best on a south orientation. (Kim 2009) On east or west
orientations, a light shelf may allow direct sunlight and cause a glare problem. To solve
this problem, people may choose to add to the depth of light shelf and thus lead to a
decrease in daylight penetration potential. (LBNL 2000) The addition of vertical fins on
east and west facades is an excellent solution to limit glare and solar gain.
2.3.4 Materials
The most widely used pre-fabricated light shelf products on high rise buildings are made
of aluminum and aluminum composite material (ACM). Aluminum and ACM are easy to
be fabricated, give light shelves lightweight property and high-quality surface. Concrete
slabs could also be used as light shelves on low rise buildings. Some semi-transparent
materials, such as frosted glass or perforated metal plates, are also used to make light
shelves, which offer interesting effects.

Most light shelf products made of opaque materials. The solid geometry blocks direct
sunshine and prevents glare in areas near windows while the high reflectance surface

32

reflect lights in to deeper part of rooms. As a result the upper surface is one of the most
critical elements of light shelf design, and it can be produced with matte or specular
finish. In 2001, Santiago compared the light shelf performance of different materials,
proving that a light shelf with high specular reflectance material mirror can have higher
illuminance level at the back of the room than low specular reflectance material
Methacrylate. (Santiago-Toma's Claros 2001) A matte finish produces diffuse reflection
without control of direction and a perfectly diffuse surface will only re-direct half of the
light into the building. A specular light shelf reflects more sunshine into rooms with
directional reflection; however mirror reflection usually casts a clear strong image on the
ceiling and causes unpredictable or negative effects on indoor lighting human comfort
and building aesthetics.

Figure 15: Light Shelves with Specular Finish (left) and Matte Finish (right)

33

Figure 16: Glare on Ceiling Caused by Glossy Reflection of Light Shelves

Since the primary intent of using light shelf in office building is to introduce more
daylight deep in rooms, the efficiency of light shelves is the most important factor for
design and increasing illuminance value of the deep part of room is the only concern of
this thesis. As a result, a mirror material for the light shelf was selected in this study.
2.3.5 Ceiling Effects
The ceiling is another part that affects light shelf performance because light is redirected
by the light shelf towards the ceiling and then reflected again into the room. Ceiling
finish, smoothness and slope could all affect the result. The specular material of the
ceiling will increase the amount of light that reflects into the room, but may also cause
some serious glare problems. There are also privacy issues with specular ceilings, which
reflect images from adjacent cubicles and occupants. So the ceiling finish is usually
diffusing white. The ceiling slope is another important characteristic. Freewan et al tested
a room with a fixed light shelf and compared the four different ceiling geometries: flat
ceiling, curved ceiling, chamfered and sloped ceiling on their effect of daylight

34

performance of the test room. A conclusion is that ceiling slope could greatly affect the
light shelf performance and a specifically designed curved ceiling could improve the light
shelf performance by increase the daylight availability and uniformity of the test room.
(A. Freewan 2008)

Figure 17: The Basic Consideration of Shaping the Ceiling Geometries and the Distance Used to Shape
Different Ceiling Geometries Based On the Light Reflected Light Shelf and Room Height (A. Freewan
2008)
2.4. Daylighting Design Assistant Tool
As mentioned above, a design assistant tool is necessary to inform the architects and
consultants of how to design an efficient light shelf system. Kleindienst et al suggested a
way to provide a guideline of utilizing anidolic light shelf in building renovation projects.
This guideline informed architects and consultant of whether or not an anidolic light shelf

35

is necessary for a specific room to be renovated. (Figure 18) This method has several
advantages. The recommendation was integrated into one table that is easy for users to
understand. The guideline also shows the relationship between room size and light shelf
configurations. (Siân Kleindienst 2006)
However, only = 30 anidolic light shelf is discussed and the indicator used in this study
is Daylight Factor which neglects the direct light and damage the results.

Figure 18: Guidelines of Anidolic Light Shelf System Design (Siân Kleindienst 2006)

Linhart et al in their research evaluate the efficiency of several anidolic light shelf
configurations which could also be used as guideline to design some specific anidolic
light shelf systems. (Friedrich Linhart 2010)
Besides guidelines, some researchers also try to create interactive tools based on popular
design software. There rarely exists such tools that support light shelf design but many

36

successful shading design tools exist. For example, Sargent showed one method called
SHADERADE that based on Rhinoceros for assessing the desirability of solar
transmittance over any potential shading volume or surface. (Jon Sargent 2011)
2.5 Summary
According to the study of the previous research, we can get the following points, which
are relevant to this research:
 A light shelf does not necessarily improve the total illuminance level of the whole
room, but it can transfer the light from the front to the back of the room and make
the light more even.
 Daylight Autonomy, which is a climate based criteria and involves a whole year
calculation, could be used to judge the performance of the light shelf.
 A light shelf will be best used on south orientation and will best improve
illuminance level at rear of the room with high specular reflectance material.
 Light shelf position and configuration will all have significant effects on light
shelf performance. But more research on what the combine effects of these factors
and more qualify and quantify analysis should be conducted.

37

Chapter 3 Methodology
This chapter introduces the computer simulation process, software parameter settings
and data analysis methodology used in this thesis. The whole work flow, especially the
Diva simulation, is introduced and discussed. The simulation setting, including building
location and orientation, room configuration, where to put the sensors and the
evaluation criteria are described.

38

3.1 Groundwork
This research is composed of two main parts. The first part is using computer simulation
tools to evaluate the daylight performance of four rooms with light shelves using a
climate based method. The second part is analysis of the simulation results of the first
part to make a light shelf design assistant tool using the data collected. Below is a
detailed list of work flow going to be processed in this research, and several important
points will be discussed in detail later. (Figure 19: Concept Workflow of This study):
1) Creating computer models of four generic test rooms that have the potential to use
light shelf improving daylighting performance. Using the Grasshopper plugin to
control the parameters configuration of the light shelf design and change them
automatically.
2) Using daylight simulation software to evaluate daylight penetration performance
of each room with each light shelf configurations.
3) Exporting light shelf performance results of each light shelf configuration into
Excel (Excel will be used as a data collector).
4) Using Excel to analyze the data and create the equation of the relationship
between light shelf configuration and the room daylight penetration.
5) Equation evaluation.
This chapter is primarily focused on the simulation. Data analysis will be discussed in
Chapter 4 and 5 in detailed.

39

Figure 19: Concept Workflow of This study
3.2 Software Preparation
In order to process the research, simulation software and data analysis software are two
of the most important tools to select. Finding appropriate ways to make the software
tools work together smoothly is a key factor.
3.2.1 Daylight Simulation Software Investigation
There exists a large number of daylight simulation software and optimization software,
an investigation needs to be conducted to find out the most appropriate one that can
complete the workflow discussed in 3.1 Ground work and achieve the objects raised in
Chapter 1.

40

Some techniques used in Computer Graphics (CG) are worth remembering when
discussing daylighting calculations. One of the important techniques that was originally
used in CG and later found its role in daylight calculation is called the ray-tracing
technique. The ray-tracing technique has two types; forward and backward ray-tracing.
Forward ray-tracing means the rays are generated at the light source and are calculated to
where they reach the eye. Backward ray-tracing means the rays are generated at eye
locations and back traced to the light source. Forward ray-tracing is more similar with the
real condition. But forward ray-tracing involves considerable complicated ray calculation
and a large portion of the results do not contribute to an image because most rays
generated by the light source do not reach the eye. Backward ray-tracing on the contrary
only calculates the rays that reach the image plane and are thus much quicker. Radiance
is lighting simulation system developed at the Lawrence Berkeley National Laboratory
(LBNL) in California by Greg Ward (1989). RADIANCE software comprises many
programs that all perform specific tasks, and sky generating is one of them. The Gensky
program simulates sky patterns of overcast sky or clear sky with and without sun. A
problem of this program is that it cannot automatically predict the full year daylight
performance. Reinhart et al proposed a new method to do a year-round calculation
called DAYSIM. It is a climate based tool and uses a time varying sky model. DAYSIM
has the advantage of improving the simulation accuracy of some complex system such as
light shelves. A problem of DAYSIM is it will not calculate heating or cooling load.
(Sandeep Kota 2009)
Many software packages claim to be able to perform the calculations discussed above.
The key concerns of selecting appropriate daylight simulation software are:

41

1) It should be evaluated and reliable.
2) It should include parametric software allowing the parameters to be easy to change.
3) It should be able to calculate Daylight Autonomy of a certain point. To get a Daylight
Autonomy value, software is required to process a further step after the illuminance
calculation (which is not included in some software packages).
For this research, four daylight simulation tools are tried and tested (Table 2)
Desktop Radiance is software package that integrates the Radiance Synthetic Imaging
System with Auto CAD release 14. Desktop Radiance includes libraries of materials,
glazing, luminaires and furnishings so you can quickly create realistic lighting models. It
has been validated by many researchers to be reliable software. However, it is not based
on parametric software and this makes it difficult to quickly and easily conduct the
calculations in this study. Also, it cannot calculate the Daylight Autonomy value of a
certain point automatically and therefore users have to calculate several different times of
a year under different sky conditions to get the Daylight Autonomy value which also adds
to the workload to this study.
Ecotect can also conduct daylight performance analysis and is based on the Radiance and
Daysim engine. The limitation of it to this study is similar with Desktop Radiance; it is
difficult to conduct a large amount of calculations, and the tool cannot obtain the daylight
autonomy number. Open studio integrated the most updated Radiance engine with the
Sketchup interface. Although Sketchup is user friendly model software, it is still difficult
for the user to control and change the object parameters with it.

42

DIVA-for-Grasshopper is a plugin which runs thermal, daylight, solar radiation, and glare
simulations. It is based on Grasshopper, which is a parametric model tool and can
conduct the daylight autonomy calculation. Diva for Grasshopper was selected for the
above reasons. The only potential limitation is that DIVA-for-Grasshopper is a relatively
new tool and still in the testing phase. Tests and evaluation of this software is necessary
to ensure the reliability of the final results and will be described in details in Chapter 4.

Table 2: Comparison of four daylight simulation software of their model platform, engine and indicator
Software Desktop
Radiance
Ecotect Open Studio Diva
Model Platform CAD Ecotect Sketchup Rhino/Grasshopper
Engine Radiance Radiance/Daysim Radiance/ Daysim Radiance/Daysim
Indicator Daylight
Autonomy
not include
Daylight
Autonomy not
include
Daylight
Autonomy not
include
Daylight Autonomy
include

Figure 20: Illuminance Level Calculation of a Living Room in Ecotect

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3.2.2 Radiance Settings
Radiance is used as the lighting simulation engine of DIVA. Radiance settings are very
important to confirm the accuracy of the daylight calculation. Primary radiance
parameters are shown in Table 3 with short description.

Table 3: Radiance Parameter and Description (Greg Ward Larson 2004)
Parameter Description
-ps Pixel sampling rate
-pt Sampling threshold
-pj Anti-aliasing jitter
-dj Source jitter
-ds Source substructuring
-dt Direct threholding
-dc Direct certainty
-dr Direct relays
-dp Direct-pretest density
-sj Specular jitter
-st Specular threshold
-ab Ambient bounces
-aa Ambient accuracy
-ar Ambient resolution
-ad Ambient divisions
-as Ambient super-samples
-lr Limit reflection
-lw Limit weight

According to the guidelines to daylight simulations in DAYSIM, an ambient bounce
describes the number of diffuse inter-reflections which will be calculated before a ray

44

path is discarded. (microshade n.d.) This parameter will greatly affect the accuracy of the
result as well as the total calculation time and should be selected cautiously.
To test the ambient bounces (ab) number’s effect on the simulation results, a test is
conducted (Figure 21). The results shows that when Ambient bounces number is two, the
light shelf almost shows no effect on the daylight performance of the room compared
with a reference room without any light shelf or shading. But the effect is significant
when the ambient bounces level is set to 8.

Figure 21: Two Ambient Bounces Numbers Have Very Different Results

A test then is conducted to find out the appropriate ambient bounce number (Figure 22).
A higher number of bounces results in a longer calculation time, so we are seeking the
fewest bounces that still obtain accurate results. We can see from figure 22 that with the
0
10
20
30
40
50
60
70
80
90
100
9 13 17 21 25 29 34 37 41 45
Daylight Autonomy (500lux)
Distance From Window
reference
room
ab=2
ab=8

45

increase of the Ambient Bounce number, the DA starts to increase and the increase
change from abrupt to smooth. The study shows that the difference between different
Ambient Bounce numbers starts to be minor when the Ambience Bounce number is 7.
Which means 7 is enough to ensure the accuracy of the results as well as to reduce the
calculation time. So 7 will be used as final Ambience Bounce number in this study.

Figure 22: Comparing Between Difference Ambient Bounce Setting of Their Daylight Autonomy

The Ambient division parameter determines the number of sample rays that are sent out
from a surface point during an ambient calculation. This parameter needs to be high if the
0
10
20
30
40
50
60
70
80
90
100
9 13 17 21 25 29 34 37 41 45
Daylight Autonomy (500lux)
Distance From Window
referen
ce
room
ab=2
ab=3
ab=4
ab=5
ab=6
ab=7
ab=8

46

luminance distribution is in a scene with a high brightness variation. An ambient
sampling parameter greater than zero determines the number of extra rays that are sent in
sample areas with a high brightness gradient.
The combination of ambient accuracy and ambient resolution parameters with the
maximum scene dimension provides a measure of how fine the luminance distribution in
a scene is calculated (microshade n.d.)
All radiance parameters are selected after careful consideration and are shown in Table 4.

Table 4: Radiance simulation parameters utilized in simulations
Radiance simulation parameters
Ambient bounces (ab) 7
Ambient accuracy (aa) 0.1
Ambient divisions (ad) 1024
Ambient super-samples (as) 64
Ambient resolution (ar) 128

3.2.3 Grasshopper
Grasshopper is selected to control the variables by number slider. (Figure 23)

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Figure 23: Light Shelf Shape Change under the Control of Grasshopper

3.2.4 Galapagos; Genetic Algorithm in Grasshopper
Galapagos is an evolutionary solver for Rhino/ Grasshopper developed by David Rutten
with McNeel & Associates. Galapagos can automatically control the grasshopper
parameters by changing the slider that has been previously introduced and then searching
for the best results that meet the requirements preset by the user. (aweida 2011) (capital
letter “A”)
This optimum result involves searching by Galapagos under certain criteria, called the
fitness number. In this study, the final object is to maximize the daylight penetration
depth of the test room. So the fitness number will be defined as the daylight autonomy
number at the rear point of the room. And Galapagos is set to find out the maximum
fitness number (Figure 24).

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Figure 24: Galapagos Is Trying to Find the Maximum Fitness Number

3.2.5 Linking Results to Excel
Excel is used as the data collector. A plugin for Grasshopper called Excel Exporter was
used. And while Galapagos is continually changing the variables for Diva to simulate, all
the selected data will be recorded in this whole process.
3.3 Simulation Conditions
3.3.1 Location
The location of the study is fixed to Los Angeles. California, USA (34.0522° N,
118.2428° W).

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3.3.2 Design of Office Module and Test Points
The design of office module and test sensors is shown in Figure 25.

Figure 25: Room Configuration and Sensors Location: Room Section (up), Room Plan (down)

The height of the office test room is fixed to 10’, which is a common office height
according to discussion in Chapter 2. The width of the office room is 20’ to reduce the

50

interruption of the reflectance of the walls. Because an office room which is deeper than
30’ can be considered as deep plan room, and this study aims to increase daylight
penetration depth of the deep office room, the depth of the office room has three settings,
35’, 40’,45’, and 50’.
The opening occupies one hundred percent of south wall. No skirt wall is used in this
study for two considerations. Firstly, architects have a preference of using wall to wall
window or glass curtain wall. Secondly, according to previous research, a skirt wall lower
than 2.5’ will rarely have an effect on daylight performance of the room.
Daylight sensors are located at 2.5’ above the floor plane to simulate the daylight
performance at a standard work plane. There are total of 11 sensors in the space. The
sensors start 5 feet from the opening and end 5 feet from the back wall. The sensors are
evenly aligned on the middle line of the room. For the final data analysis, only the
sensor at the rear of the room is used to evaluate the daylight penetration depth. The other
10 sensors are calculated to get a total picture of the daylight performance of the room.
The evaluation criteria used to compare different light shelf strategies in this study is
daylight penetration depth of the room, which is defined as the Daylight Autonomy value
of the point that is 5’ away from back wall of the test room. This number is set as the
fitness number in Galapagos to make the workflow automatically find out the most
efficient light shelf strategies. This criteria is also used in Excel to rank all the light shelf
strategies as the Galapagos can only find out the optimum one, Excel can record all the
strategies for later data analysis work. The evaluation process will be discussed in more
detail in Chapter 5.

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3.3.3 Schedule
The calculation schedule is set to weekdays from 9am to 5pm which is typical office
hours.
3.4 Research variables
The factors that affect the performance of light shelf have already been discussed in
Chapter 2 and can be summarized as follows:
1) Room configurations and room interior material
2) Ceiling shape
3) Light shelf configuration and material
4) Building location and orientation
5) Opening configurations and material
This study aims at evaluation of the effect of different light shelf configurations on room
daylight penetration depth. After careful selection, the factors that affect light shelf
performance were then categorized into independent variables, dependent variables and
constants.
The main variables that are included in this study are shown in Table 5. The research
variables are consisted of three parts: variables of office space includes opening,
variables of light shelf, and daylight penetration depth.
The space orientation and interior reflectance were kept continuous during tests. The
space has a fixed size window for which transmittance is continuous also.

52

The main independent variables of the test are light shelf configuration parameters and
the room depth. The main dependent variable in this study is daylight penetration depth
of the room. This research is focused on find out how light shelf configuration and room
depth could affect daylight penetration depth of rooms. The definition of each light shelf
variable will be discussed in detail in later paragraphs.

Table 5: Dependent and Independent Variables and Constants for Parametric Daylight Simulation
Type Name Variable Type
Office Space
Orientation Constant
Interior Reflectance Constant
Depth Independent Variables
Width Constant
Height Constant
Glazing
Window size Constant
Transmittance Constant
Light Shelf
Upper Surface Reflectance Constant
Lower Surface Reflectance Constant
Length Constant
Width Independent Variables

53

Curvature Independent Variables
Tilt Angle Independent Variables
Height Independent Variables
Interior Daylight
Condition
Daylight Penetration Depth Dependent Variables

3.4.1 Independent variables
The independent variables of the study include light shelf parameters (tilt angle,
curvature, height, width) and room depth. The total test amount and case amount of
different light shelf variables is shown in Table 6. Figure 26 gives the visual concept of
the variations of light shelf parameters. The definition of each light shelf parameter could
be seen in Figure 27 to Figure 29.

Table 6: Test Cases of Independent Variables
Type Name Case Total Number
Light Shelf
Angle (degree) 0 15 30 3
Curvature (degree) 0 15 30 3
Height (feet) 7 8 2
Width(feet) 1 2 3 4 4

54

Room Depth(feet) 30 40 50 3
Total Cases=3×3×2×4×3=216

Figure 26: Concept Diagrams Show Light Shelf Variables Comparisons

55

3.4.1.1 Light shelf curvature
The light shelf curvature is measured as degree α. To define the light shelf curvature in
this study, first the midpoint and the endpoints of the light shelf is identified, then two
lines that connected each endpoint with the midpoint are identified, the angle of these two
lines is defined as the light shelf curvature parameter in this study. (Figure 27)

Figure 27: Diagram Shows Light Shelf Curvature (α) Definition

3.4.1.2 Light shelf tilt angle
Light shelf tilt angle is measured as degree . Tilt angle is defined as the angle between
the extension line of two endpoints and the horizontal line. The tilt angle and curvature
parameter are combined to define the complex shape of curved light shelf. (Figure 28)

56

Figure 28: Diagram Show Light Shelf Curvature and Tilt Angle Definition

The definition of light shelf configuration in this study has some limitation; the light shelf
curve is not tangent to the horizontal at the end point. Figure 29 gives a new definition of
the light shelf configuration for researchers to reference in future study. The light shelf
curve is an arc, and it is tangent to the horizontal at the end point. The light shelf
configuration could be defined by two variables, the chord length of the light shelf arc D
and the tilt angle .

57

Figure 29: New Light Shelf Configuration Definition for Future Study: Light Shelf is Tangent to the
Horizontal at the End Point

3.4.1.3 Light shelf width
Light shelf width (w) is defined by the line length of the horizontal flat light shelf or the
arc length of the curved light shelf with the consideration of their equal material cost
(Figure 30). So if a horizontal flat light shelf has the same width with a curved light shelf,
their shadow length will not be the same (Figure 31) nor will the intercepted sunlight be
equal.

58

Figure 30: Diagram Shows General Width (W) Definition of Horizontal Light Shelf

Figure 31: Two Light Shelves with the Same Width

The light shelf width definition in this study can only ensure the same width light shelves
have the same surface area so they have the same material costs. But this definition
cannot make sure they have the same effective width, which means they will have the

59

same amount of intercepted sunlight. A future study could adjust this definition and use
the same effective width (Figure 32) instead of the same material area.

Figure 32: Light Shelf Width New Definition for Future Study Reference: Effective Width

3.4.1.4 Light shelf height
The light shelf height is defined as the height from the floor level to the lowest endpoint
of the light shelf (Figure 33). Curved light shelf height is defined as the distance between
the intersection of light shelf and the opening and the floor plan.

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Figure 33: Diagrams shows General Height (H) Definition of Horizontal Light Shelf

3.4.2 Dependent variables
The main dependent variable in this study is the daylight penetration depth which already
been discussed in section 3.3.2 Design of Office Module and Test points.
3.4.3 Constants
The test room height and width are set as constants by considering the basic module
dimension of an office space. The test room is set to be in the middle level of a high-rise
office building. So floor reflectance wouldn’t significantly affect the result.
The reflectance of room floors, walls, ceilings are described in Table 7 and are all set to
recommended reflectance level provided by PHILIPS (Philips 2013).
The orientation of the opening for the office space is due south, which is the optimum
orientation to use a light shelf as described in Chapter 2. The size of the opening is
constant at 200 square feet. Light shelf length is same with the opening length. The light
shelf surface material is set to be mirror material which, as demonstrated in Chapter 2,

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can greatly improve its performance. To simulate the real condition, the metal material is
used as a modifier (Table 8).

Table 7: Floor, Wall, Ceiling and Ground Reflectance of Test Room

Table 8: Light Shelf Upper Surface Radiance Material in This Study
VOID METAL MYSHEETMETAL VOID MIRROR MYSHEETMIRROR

0

0

5 .9 .9 .9 .8 0
1 MYSHEETMETAL

0

3 .72 .72 .72

3.5 Design Tool Documentation
The workflow is documented here with short descriptions.
Material properties
Floors 20% Diffuse reflectance
Walls 50% Diffuse reflectance
Ceilings 80% Diffuse reflectance
Outside ground 20% Diffuse reflectance

62

Figure 34 shows the components that will record the light shelf independent variables and
write each of the variables in Excel. The number slider will control which sheet the data
will be recorded in Excel. The text panel controls the file address of the Excel for
Grasshopper to read through.

Figure 34: Excel Write Components in Grasshopper

Figure 35 and Figure 36 shows the number sliders that control the independent variables
of a light shelf and the room; they will be automatically adjusted by Galapagos.

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Figure 35: Variables Control Slider in Grasshopper

Figure 36: Variables Control Slider in Grasshopper

Figure 37 shows the Galapagos component that connects with the number sliders to
control the light shelf variables. It also shows the room configuration components
(window, floor, wall and ceiling) and the component that control their material.

64

Figure 37: Galapagos Connects with Grasshopper Components

Figure 38 shows the grasshopper components that create a light shelf.

Figure 38: Grasshopper Definition of Light Shelf Configuration

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Figure 39 shows the grasshopper components that define the calculation point’s position
and amount.

Figure 39: the Grasshopper Definition of Sensor Points

Figure 40 shows the DIVA calculation component that connects with all the geometry.
The DIVA calculation component controls all the radiance setting and calculation
settings
.
Figure 40: DIVA Calculation Components in Grasshopper

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Figure 41 shows the Excel writing components that functioned as recording the output
from DIVA calculation and writing them in Excel.

Figure 41: Excel Write Components

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Chapter 4 Software Evaluation Problems and Suggestions

Light shelf study involves indirect light simulation, which is more complex than simple
shading simulation. As a result, it is easy for small errors to occur and lead to inaccurate
results. Moreover, DIVA is relatively new software and has not been fully validated.
These all add to the difficulty for the study to get accurate simulation results. This chapter
mainly focuses on introduction and discussion of the problems and some interesting
points found during the author’s simulation and evaluation process for future researcher’s
reference.

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4.1 Evaluation Methodology
4.1.1 Test Modules
Five models with different shadings or light shelves are set up in DIVA for Rhino (Figure
42).

Figure 42: Test Models: Test Room 1 without Any Shading (Above Left), Test Room 2 with 1” Shading
(Above Right), Test Room 3 with 8’ Shading (Middle Left), Test Room 4 with 100’ Shading (Middle
Right), Test Room 5 with 8’ Light Shelf (Bottom)

69

The room modules are 50’ depth, 10’ height, and 35’ width. They are south oriented with
wall to wall windows without glass in order to simplify the process. A total of five test
rooms will test normal conditions, and some extreme situations also have been set up as
reference although they would be unlikely to happen in real practice.
Test room 1 without any shading is the reference room. Test room 2 with 1” shading is to
test the minimum light shelf width situation, which should have minimal effect on the
room and should show similar numbers on DA simulation. Test room 3 with 8’ shading is
to test normal shading situation, test room 5 with 8’ light shelf is to test normal light shelf
situation. Comparing test 3 and test 5 could test whether or not indirect light redirected by
the light shelf has been calculated by the software. Test room 4 with 100’ shading is to
test the maximum light shelf width situation and should show lowest DA value since
more light are blocked by the long shading slab.
4.1.2 Simulation Conditions
As mentioned in Chapter 3, DIVA for Grasshopper is selected as the simulation tool for
this study as it can perform large amount of simulations with the help of Galapagos.
However, DIVA for Grasshopper requires more extra software skills and settings than
DIVA for Rhino, which makes DIVA for Grasshopper harder to find where the problem
lies in the DIVA software, itself. So in this chapter, DIVA for Rhino is used to run
evaluation tests as it is easier to use and these tests don't require a large amount of
simulations. The performance criterion is Daylight Autonomy (>500lux) which

70

represents the percent of the time of one year that the illuminance level of a certain point
is higher than 500 lux. Settings of simulation are shown in the following tables.

Table 9: Material Properties of the Test Module

Table 10: Radiance Simulation Parameters
Radiance simulation parameters
Ambient bounces (ab) 7
Ambient accuracy (aa) 0.1
Ambient divisions (ad) 1024
Ambient super-samples (as) 64
Ambient resolution (ar) 128

Material properties
Floors 20% Diffuse reflectance
Walls 50% Diffuse reflectance
Ceilings 80% Diffuse reflectance
Outside ground 20% Diffuse reflectance
Light Shelf void mirror silver mirror
0
0
3 .9 .9 .9

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Figure 43: Simulation Settings in DIVA

4.2. Potential Problems
4.2.1 Material
Diva for Rhino uses the Radiance lighting simulation engine and reads Radiance material
files. The light shelf built-in evaluation models are built as rectangular planar objects and
assigned with solid material of high mirror reflectance on top of them. As discussed in

72

Chapter 2, a high mirror reflectance material could maximize light shelf performance and
is easy for results observation in this research. However, defining mirror material in
DIVA requires more careful consideration without causing errors in results.
In this test, simulations were run with mirror material shown as below.
Mirror Material Assigned to Test Light Shelves:
void mirror silver_mirror
0
0
3 .9 .9 .9

Figure 44 and Figure 45 show the Daylight Autonomy calculation results for test room 1
without any shading and test room 4 with 100’ shading. The figure only shows the north
part of the room, which is the part of the room furthest from the window. Each point
represents the DA value of the sensor points that on the work plane. Comparing these two
results, we can see test room 1 has a lower average DA than test room 2, which obviously
goes against the common sense.
100’ shading is really long and it should block most of the direct sunlight. It is almost
impossible for a room of 50’ depth and equipped with a 100’ shading that has 40% DA
(>500lux) at rear of the room.

73

Figure 44: DIVA Calculation Results of Test Room 1 without Any Shading

Figure 45: DIVA Calculation Results of Test Room 4 with 100’ Shading

74

The problem is then uploaded to DIVA discussion group and the answers are shown
below.
The material of the light shelf used in this test is the major cause of this simulation error.
The former material that caused the simulation error is the mirror material, which will
produce virtual source reflections. This material should be used sparingly, as it may cause
the light source calculation to blow up if it is applied to many small surfaces. This
material is only supported for flat surfaces such as polygons and rings. The arguments are
simply the RGB reflectance values, which should be between 0 and 1. An optional string
argument may be used such as “illum type” to specify a different material to be used for
shading non-source rays. If this alternate material is given as "void", then the mirror
surface will be invisible. This is only appropriate if the surface hides other (more detailed)
geometry with the same overall reflectance.
As a result, combined material with both metal and mirror should be used and a more
realistic definition of a mirrored light shelf is the below (from Lars Grobe):
void metal mySheetMetal
0
0
5 .9 .9 .9 .8 0

void mirror mySheetMirror
1 mySheetMetal
0
3 .72 .72 .72
This adjusted material for light shelf still uses mirror material, but also uses metal
material as a modifier.

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4.2.2 Multiple Test Cells in One Simulation Model
Another problem deserves concern is the problem caused by multiple test cells calculated
together in one simulation.
At first, 5 test cells are calculated in one simulation in DIVA for Rhino to make the
process run faster. But the results seem doubtable

Figure 46: DIVA Calculation Results of Test Room 4 with 100’ Shading

From this diagram we can see, the room with light shelf could reach almost 95% DA at
43.75 feet of the room. This seems too high for a side lit room of 50’ depth. The problem
is proved to be related to multiple test cells in one simulation model. Two comparison
tests are performed, as shown in Figure 47. The grey plane is the ground plane. The first
test is to perform a DIVA calculation of five test cells in one simulation and the second

76

test only includes one test cell in the same place in one simulation. The other settings all
stay constant in these two simulations. The calculation results are shown in Figure 48 and
Figure 49. The simulation results for that certain room that stayed in the same position
should stay constant in the two tests. However, we found that when simulation changes
from all five in one simulation to one test cell in one simulation, the simulation results of
that certain test cell (with red box) has changed. The cell has not changed. Only then
number of cells being tested has changed. Yet the results for that cell have changed.

Figure 47: Change from Multiple Models in One Set to One Model Per Calculation

77

Figure 48: DIVA Calculation Results of Test 1 with Five Models in one Simulation

Figure 49: DIVA Calculation Results of Test 2 with Only One Model in the same place in one Simulation

78

This might be caused by the DIVA inner calculation method. As a result, to ensure the
accuracy of the simulation results of DIVA, in each simulation, only one test cell should
be included.
4.2.3 Ground Plane Size and Test Module Position
The DIVA tests of the author also show that the location of test cells according to the
ground plane has an effect on the simulation results (Figure 50). Also, the size of the
ground plane could have some effect on the simulation results (Figure 51). These two
issues are not introduced in DIVA websites or any instructions thus users may not be
aware of. This is because light reflected from the ground plane will reach the ceiling and
then be re-reflected inside the building. The size of the ground plane may also change
how some of Radiance's ambient parameters will act (but this should be a minor effect in
most cases).
In summary, in order to perform a relatively accurate strategies comparison using DIVA
for Rhino or Grasshopper, researchers have to build each test cell or building in different
models individually and center them. The ground plane should keep constant in each
simulation. According to the answer from DIVA Discussion Group, there is not a good
rule of thumb for how big such a plane should be, but maybe a good starting point is 10
times larger than the building depth.

79

Figure 50: Diagrams Shows the Change of Test Model Position according to the Ground Plane in This
Study

Figure 51: Diagram Shows the Change of the Ground Plane Size in This Study

80

Chapter 5 Daylighting Simulation Results and Analysis
A light shelf can increase daylight penetration depth of the room and thus save building
energy. The light shelf configuration is a key factor that affects room daylighting
performance. In this chapter, four rooms with light shelves of 288 different
configurations will be simulated and the results are presented and analyzed.

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5.1 Preparation Tests and Data Analysis Methods
5.1.1 Room Depth Test
Light shelves can improve the penetration depth of daylighting in rooms, but it is not a
universal good choice to all rooms. Some small depth rooms are already bright enough
that they do not need a light shelf, while some deep rooms may be so deep that the light
shelf cannot help the entire room. Room depth is one key factor to decide whether a light
shelf should be used and Figure 52 below shows the comparisons of rooms without light
shelves and with light shelves.

Figure 52: Diagram Shows the Relationship between Room Depth and Daylight Autonomy (DA) at rear of
the room for room with and without light shelves

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25 feet depth room without any light shelf already has 95% Daylight Autonomy at rear of
the room and 30 feet depth room already has 89% Daylight Autonomy at rear of the room.
For rooms less than 30’ deep, light shelf will not greatly improve daylight penetration
depth because they already have enough daylight. Also, a light shelf will not have great
impact on increasing Daylight Autonomy value for the room deeper than 50 feet. For
instance, a 55’ deep room, light shelf could only increase Daylight Autonomy at rear of
the room from 0% to 2%, which is far away from sufficient daylight requirement.
Because this study aims at evaluating light shelf impact on daylight penetration depth of
the room, so rooms that are already bright enough or rooms that are too deep for light
shelves to function will be excluded. Therefore, rooms of 35’, 40’, 45’ and 50’ depth are
selected as test cases for further simulation and analysis.
5.1.2 Light Shelf and Overhang Shading Comparison Test
A light shelf does not necessarily improve indoor daylighting environment. It may reduce
the total amount of light getting in to a room. But compared to an overhang, which is the
most widely used horizontal sunlight control strategy, a light shelf generally shows better
results on improving daylight penetration depth. Figure 53 below shows how different
daylighting strategies could affect DA values in a 35’ deep room.

83

Figure 53: Daylight Autonomy Distribution Diagram of the Rooms Using Four Different Strategies:
Without Light Shelf, With Overhang Shading, With Flat Horizontal Light Shelf, With Curved Light Shelf

According to the simulation results, a flat horizontal light shelf will not increase the
Daylight Autonomy value at rear of the room comparing with the reference room without
any light shelf or shading. However, the overhang shading with the same length could
greatly decrease the Daylight Autonomy at rear of the room. This means a flat horizontal
light shelf could redirect the light into the back, but not necessary increase the daylight
penetration depth. This observation complies with most statements concluded by other
researchers and explains why some people think light shelves don’t work well in Los
Angeles. However, if the light shelf configuration changed to curved and tilted, the
Daylight Autonomy could greatly increase at rear of the room. To understand how light
shelf variables affect a light shelf’s performance, more tests are performed. This study
will mainly focused on evaluation and analysis four variables (width, height, curvature
and tilt angle) of a light shelf and their impact on the daylight penetration depth.
0
10
20
30
40
50
60
70
80
90
100
5 7.5 10 12.5 15 17.5 20 22.5 25 27.5 30
DA(>500)
Distance From Window(feet)
Reference
Room without
Light Shelf
Room with
Overhang
Shading
Room with
Flat Horizontal
Light Shelf
Room with
Curved Light
Shelf

84

5.1.3 Data Analysis Methods
A total of 288 cases were tested using four rooms with 72 different configurations for
each room. These were simulated using DIVA and the results are presented and analyzed
in this chapter.
As previously mentioned in Chapter 3, the evaluation method assesses the quantity of
daylight inside the office space in terms of depth of daylight penetration. The Daylight
Autonomy value of the sensor point at 5 feet away from the room back wall is used as the
performance criteria to reflect the daylight penetration depth of the room.
Results are presented by comparing the test cases of the room with different
configuration light shelves to the pre-defined performance criteria and base cases of the
room without any light shelf.
The data analysis in this chapter mainly consists of two parts. First part is to evaluate
different variables’ impact on daylight penetration depth. In this part, we are going to
compare different light shelf’s performance in each test rooms and help designers find
out best light shelves from lighting point of view. Second part is to evaluate how these
variables impact could change with the change of room depth. In this chapter, we are
going to discover the relationships between each variable and Daylight Autonomy, and
decide which variable has a stronger effect on daylight performance.

85

5.1.4 Charts and Diagrams
Because there are four variables of light shelves and one variable of room in this study, to
simplify the results and make them easy to analyze, all 288 simulation cases are first
divided into four main categories according to room depth.
In the first part of data analysis, the results are then categorized by light shelf height.
Figure 54 presents a sample chart created to show the relationship between Daylight
Autonomy and light shelf curvature and tilt angle. Each diagram represents 9 specific test
combinations that were simulated by DIVA. The vertical axis on the left represents the
Daylight Autonomy value of the sensor at 5’ away from the room back wall, which range
changed according to the room depth. In order to help us evaluate the light shelf impact,
the lower limitation of the range is the same with the DA of the room without any light
shelf.
The horizontal axis represents the light shelf curvature, which ranges from 0 to 30
degrees while the depth axis (vertical axis on the right) represents the light shelf tilt angle,
which also ranges from 0 to 30 degrees. Light shelves are divided into 4 groups and the
color represents the degree of increase of DA that caused by light shelves and therefore
informs whether or not light shelves are recommended by the way that is easy for
architects to understand. Blue means that a light shelf in this range is not recommended
because it has the similar or only small improved performance of the reference room,
while green means that a light shelf in this range is relatively not recommended also.
Red indicates a light shelf in this range is recommended and yellow means a light shelf

86

combination in this range is highly recommended due to its’ excellent performance on
improving daylight penetration depth.

Figure 54: Sample Chart for Daylight Autonomy Analysis

This case shows the performance variation of different light shelf curvature and light
shelf angle. The light shelf depth and height are kept constant in each diagram.
The baseline DA, DA value of the room without any light shelf, in this case is 45, and the
best light shelf combination could increase room DA to 75 which already met the IES
requirement of sufficient daylighting of an office room.
In this specific case (35’ depth room with 2’ depth and 7’ height light shelf), a light shelf
performs best when the light shelf angle is 30 degree. Light shelf curvature only has a
small impact on the final results. Light shelf performance is primarily decided by the tilt
angle and DA will increase while the tilt angle gets bigger. This diagram also informs
that flat horizontal light shelves in this situation do not perform well.
0
15
30
45
53
61
69
77
0
15
30
Light Shelf Angle
Daylight Autonomy at
5' from Back Wall
Light Shelf Curvature
7' High, 2' Depth Light Shelf

87

Figure 55 presents a sample chart for the relationship analysis between Daylight
Autonomy and light shelf width. This chart shows tested results of 35’ room, with a 7’
high light shelf, and all the tested results are grouped by light shelf width. Each diagram
represents all 36 light shelf combinations of certain height in a certain depth room that
are simulated by DIVA. The vertical axis represents the Daylight Autonomy at 5’ away
from the room back wall. The horizontal axis represents the light shelf width, which has
four values, 1 foot, 2 feet, 3 feet and 4 feet. Each blue point represents one specific
combination of light shelf variables that simulated by DIVA and some combinations have
the same Daylight Autonomy so there are some overlaps of these points. The points with
the highest and lowest Daylight Autonomy are labeled with their value. The red dashed
line represents the baseline DA of the reference room without any light shelf.

Figure 55: Diagram Represent the Relationship between DA and Light Shelf Width

66
45
71
42
74
43
75
42
40
50
60
70
80
1 2 3 4
DA at 5' away from the back wall
Light Shelf Width (feet)
Reference Line:
DA=45

88

This case shows the performance variation of different light shelf width. The light shelf
height and room depth keep constant in each diagram. The baseline of Daylight
Autonomy in this case is 45 and most points are located above this line while some of
them below this line. 4’ wide light shelves show bigger DA variation. This means light
shelf width, from 1’ to 4’, is not the only key variable that decides whether light shelf
will improve lighting performance of a room and light shelf width just magnifies light
shelf impacts. Designer still has to consider other variables to design a high performance
light shelf. 4 feet width light shelf has the highest DA value of 75, while best case of 1
foot light shelf has the DA of 66. Lowest DA of each light shelf width is very close to
each other.
The second part analysis is using performance curve to represent the relationship
tendency between light shelf variables and DA at rear of the room. Each Performance
Curve represents a single independent variable. A polynomial having only a single
independent variable represents a one-dimensional relationship between a condition (light
shelf variables) and response (DA at 5’ away from the room back wall). Figure 56 is a
sample chart including the performance curve that represents the relationship between
light shelf width and DA.

89

Figure 56: Sample Chart of Light Shelf Variable Tendency Analysis

The performance curve in this diagram is Quadratic Curve which means a performance
curve having an order or degree of 2. For this specific depth room, light shelf width has a
positive impact on the DA. The DA will increase as light shelf width gets bigger.
30
40
50
60
70
80
1 2 3 4
DA at 5' away from the back
wall
Light Shelf Width
35' Depth Room

90

5.2 35 feet Depth Room
5.2.1 Light Shelf Height 7 feet

Figure 57: Diagram Shows Relationship Between Light Shelf Variables (Curvature and Tilt Angle) and
Daylight Autonomy at 5 Feet from the Back Wall of the Room: 35 feet Depth Room, 7 Feet Height Light
Shelf

For 35 feet deep room with 7 feet height light shelf and 10 feet height ceiling, DA is
primarily decided by light shelf angle and DA value increases when light shelf tilt angle
gets bigger from 0 to 30 . DA reaches the highest value when light shelf tilt angle is 30
degree. This also shows that flat horizontal light shelf will not function well for room in
0
15
30
45
53
61
69
77
0
15
30
Light Shelf Angle
Daylight Autonomy at
5' from Back Wall
Light Shelf Curvature
7' High, 1' Depth Light Shelf
0
15
30
45
53
61
69
77
0
15
30
Light Shelf Angle
Daylight Autonomy at
5' from Back Wall
Light Shelf Curvature
7' High, 2' Depth Light Shelf
0
30
45
53
61
69
77
0
15
30
Light Shelf Angle
Daylight Autonomy at
5' from Back Wall
Light Shelf Curvature
7' High, 3' Depth Light Shelf
0
30
45
55
65
75
85
0
15
30
Light Shelf Angle
Daylight Autonomy at
5' from Back Wall
Light Shelf Curvature
7' High, 4' Depth Light Shelf

91

this depth. The impact of light shelf curvature on DA seems not noticeable in this
diagram. Comparing these four diagrams, we can see light shelf width also could affect
DA at rear of the room; the highest DA happened at four feet light shelf and 1 foot light
shelf doesn’t have the yellow color area which means the light shelf is highly
recommended. Figure 58 gives the further analysis of the effect of light shelf width.

Figure 58: Diagram Shows Relationship between Light Shelf Variable (Width) and Daylight Autonomy at
5 Feet from the Back Wall of the Test Room: 35 feet Depth Room, 7 Feet Height Light Shelf

This case shows the performance variation of different light shelf width. The light shelf
height and room depth keep constant in each diagram. The baseline of Daylight
Autonomy in this case is 45 and most points are located above this line, while some of
them below this line. This means light shelf width is not the only key variable that affects
its performance; designer still has to consider other variables to design a high
performance light shelf. 4 feet width light shelf has the highest DA value of 75, while
66
45
71
42
74
43
75
42
40
50
60
70
80
1 2 3 4
DA at 5' away from the back wall
Light Shelf Width (feet)
Reference
Line: DA=45

92

best case of 1 foot light shelf has the DA of 66. Lowest DA of each light shelf width is
very close to each other.

93

5.2.2 Light Shelf Height 8 feet

Figure 59: Diagram Shows Relationship Between Light Shelf Variables (Curvature and Tilt Angle) and
Daylight Autonomy at 5 Feet from the Back Wall of the Room: 35 feet Depth Room, 8 Feet Height Light
Shelf

For 35 feet depth room with 8 feet height light shelf and 10 feet height ceiling, DA is also
primarily decided by light shelf angle, from 0 to 30 , DA increases when light shelf tilt
angle gets bigger. DA reaches the highest value when light shelf tilt angle is 30 degree.
This also shows that flat horizontal light shelf will not function well for room in this
depth. The impact of light shelf curvature on DA seems not noticeable in this diagram.
0
30
15
25
35
45
55
0
15
30
Light Shelf Angle
Daylight Autonomy at
5' from Back Wall
Light Shelf Curvature
8' Height, 1' Depth Light Shelf
0
30
15
25
35
45
55
0
15
30
Light Shelf Angle
Daylight Autonomy at
5' from Back Wall
Light Shelf Curvature
8' Height, 2' Depth Light Shelf
30
0
45
53
61
69
77
0
15
30
Light Shelf Angle
Daylight Autonomy at
5' from Back Wall
Light Shelf Curvature
8' High, 3' Depth Light Shelf
30
15
0
45
53
61
69
77
0
15
30
Light Shelf Angle
Daylight Autonomy at
5' from Back Wall
Light Shelf Curvature
8' High, 4' Depth Light Shelf

94

Comparing these four diagrams, we can see light shelf width also could affect DA at rear
of the room, the highest DA happened at four feet light shelf and 1 foot and 2 feet width
light shelf doesn’t have the yellow color area which means the light shelf is highly
recommended. Figure 60 gives the further analysis of the effect of light shelf width.

Figure 60: Diagram Shows Relationship between Light Shelf Variable (Width) and Daylight Autonomy at
5 Feet from the Back Wall of the Room: 35 feet Depth Room, 8 Feet Height Light Shelf

This case shows the performance variation of different light shelf width. The light shelf
height and room depth keep constant in each diagram. As previous diagram, we can get
the information from this diagram that light shelf width is not the only key factor that
affects DA. 4 feet width light shelf has the highest DA value of 72, while best case of 1
foot light shelf has the DA of 66. Lowest DA of each light shelf width is very close to
each other.
66
44
70
42
71
40
72
54
40
50
60
70
80
1 2 3 4
DA at 5' away from the back wall
Light Shelf Width (feet)
Reference Line:
DA=45

95

Table 11: Light Shelf Combinations Rank for 35 feet Depth Room
Rank
Light
Shelf
Height
(feet)
Light
Shelf
Width
(feet)
Light
Shelf
Curvature
Light
Shelf
Tilt
Angle
D
A
Rank
Light
Shelf
Height
(feet)
Light
Shelf
Width
(feet)
Light
Shelf
Curvature
Light
Shelf
Tilt
Angle
D
A
1 7 4 0 30 7
5
37 8 1 0 30 5
9 2 7 3 0 30 7
4
38 7 1 15 15 5
7 3 7 3 15 30 7
4
39 8 1 30 15 5
7 4 7 3 30 30 7
4
40 8 2 15 15 5
6 5 7 4 15 30 7
4
41 8 4 15 15 5
6 6 7 4 30 30 7
3
42 7 1 0 15 5
5 7 8 4 30 30 7
2
43 8 3 15 15 5
5 8 7 2 15 30 7
1
44 8 4 0 15 5
4 9 7 2 30 30 7
1
45 8 3 0 15 5
3 10 8 4 15 30 7
1
46 8 1 15 15 5
1 11 7 2 0 30 7
0
47 8 2 0 15 5
1 12 8 3 30 30 7
0
48 8 1 0 15 5
0 13 8 3 15 30 7
0
49 7 1 15 0 4
9 14 7 3 0 15 6
9
50 7 3 30 0 4
6 15 7 4 15 15 6
9
51 7 1 30 0 4
6 16 8 2 15 30 6
8
52 7 2 30 0 4
6 17 8 4 0 30 6
8
53 7 4 30 0 4
5 18 7 3 15 15 6
7
54 7 1 0 0 4
5 19 7 4 30 15 6
7
55 7 2 15 0 4
5 20 8 3 0 30 6
7
56 8 1 0 0 4
5 21 7 2 15 15 6
6
57 8 1 30 0 4
5 22 7 3 30 15 6
6
58 7 4 0 0 4
4 23 7 4 0 15 6
6
59 8 1 15 0 4
4 24 8 2 0 30 6
6
60 7 3 0 0 4
3 25 8 2 30 30 6
6
61 7 3 15 0 4
3 26 7 2 0 15 6
5
62 7 2 0 0 4
2 27 7 2 30 15 6
5
63 7 4 15 0 4
2 28 7 1 0 30 6
4
64 8 2 0 0 4
2 29 7 1 15 30 6
4
65 8 2 15 0 4
2 30 7 1 30 30 6
4
66 8 2 30 0 4
2 31 8 1 15 30 6
3
67 8 3 0 0 4
0 32 8 4 30 15 6
2
68 8 3 15 0 3
9 33 7 1 30 15 6
1
69 8 4 0 0 3
8 34 8 3 30 15 6
1
70 8 3 30 0 3
7 35 8 1 30 30 6
0
71 8 4 30 0 3
7 36 8 2 30 15 6
0
72 8 4 15 0 3
5

96

5.3 40 feet Depth Room
5.3.1 Light Shelf Height 7 feet

Figure 61: Diagram Shows Relationship Between Light Shelf Variables (Curvature and Tilt Angle) and
Daylight Autonomy at 5 Feet from the Back Wall of the Test Room: 40 feet Depth Room, 7 Feet Height
Light Shelf

Same as 35 feet depth room, for 40 feet depth room with 7 feet height light shelf and 10
feet height ceiling, DA is primarily decided by light shelf angle, DA increases when light
shelf tilt angle gets bigger from 0 to 30 ,. This also shows that flat horizontal light shelf
will not function well for room in this depth. In this case, the impact of light shelf
0
15
30
15
25
35
45
55
0
15
30
Light Shelf Angle
Daylight Autonomy
at 5' from Back Wall
Light Shelf Curvature
7' Height, 1' Depth Light Shelf
0
15
30
15
25
35
45
55
0
15
30
Light Shelf Angle
Daylight Autonomy
at 5' from Back Wall
Light Shelf Curvature
7' Height, 2' Depth Light Shelf
0
15
30
15
25
35
45
55
0
15
30
Light Shelf Angle
Daylight Autonomy
at 5' from Back Wall
Light Shelf Curvature
7' Height, 3' Depth Light Shelf
0
30
15
25
35
45
55
0
15
30
Light Shelf Angle
Daylight Autonomy
at 5' from Back Wall
Light Shelf Curvature
7' Height, 4' Depth Light Shelf

97

curvature on DA is still not noticeable. Although DA reaches the highest value when
light shelf tilt angle is 30 degree and curvature is 15 degree, there is no clear relationship
between light shelf curvature and DA. Comparing these four diagrams, we can see light
shelf width also could affect DA at rear of the room, the highest DA happened at four feet
light shelf and 1 foot and 2 feet light shelf doesn’t have the yellow color area which
means the light shelf is highly recommended. Figure 62 gives the further analysis of the
effect of light shelf width.

Figure 62: Diagram Shows Relationship between Light Shelf Variable (Width) and Daylight Autonomy at
5 Feet from the Back Wall of the Test Room: 40 feet Depth Room, 7 Feet Height Light Shelf

The baseline of Daylight Autonomy in this case is 25. 4 feet width light shelf has the
highest DA value of 52, while the best case of 1 foot light shelf has the DA of 36. This
means in this case the increase of light shelf width has a noticeable impact on DA
improvement.
52
17
49
19
44
22
36
25
0
10
20
30
40
50
60
1 2 3 4
DA at 5' away from the back wall
Light Shelf Width (feet)
Reference Line :
DA=25

98

5.3.2 Light Shelf Height 8 feet

Figure 63: Diagram Shows Relationship Between Light Shelf Variables (Curvature and Tilt Angle) and
Daylight Autonomy at 5 Feet from the Back Wall of the Test Room: 40 feet Depth Room, 8 Feet Height
Light Shelf

For 40 feet depth room with 8 feet height light shelf and 10 feet height ceiling, DA is
primarily decided by light shelf angle, DA increases when light shelf tilt angle gets
bigger, from 0 to 30 . DA reaches the highest value when light shelf tilt angle is 30
0
30
15
25
35
45
55
0
15
30
Light Shelf Angle
Daylight Autonomy
at 5' from Back Wall
Light Shelf Curvature
8' Height, 1' Depth Light Shelf
0
15
30
15
25
35
45
55
0
15
30
Light Shelf Angle
Daylight Autonomy
at 5' from Back Wall
Light Shelf Curvature
8' Height, 2' Depth Light Shelf
30
15
25
35
45
55
0
15
30
Light Shelf Angle
Daylight Autonomy
at 5' from Back Wall
Light Shelf Curvature
8' Height, 3' Depth Light Shelf
30 15
25
35
45
55
0
15
30
Light Shelf Angle
Daylight Autonomy
at 5' from Back Wall
Light Shelf Curvature
8' Height, 4' Depth Light Shelf

99

degree. This also shows that flat horizontal light shelf will not function well for room in
this depth. The best combination is 30 degree tilt angle and 15 degree curvature. But for
other cases, light shelf curvature doesn't have a clear relationship with DA at rear of the
room.

Figure 64: Diagram Shows Relationship between Light Shelf Variable (Width) and Daylight Autonomy at
5 Feet from the Back Wall of the Test Room: 40 feet Depth Room, 8 Feet Height Light Shelf

This case shows the performance variation of different light shelf width. The light shelf
height and room depth keep constant in each diagram. Light shelf width is a factor that
affects DA. 4 feet width light shelf has the highest DA value of 44, while best case of 1
foot light shelf has the DA of 32. In addition, we can get the information from this
diagram that light shelf width is not the only key factor that affects DA.

44
19
42
20
39
22
32
23
0
10
20
30
40
50
60
1 2 3 4
DA at 5' away from the back wall
Light Shelf Width (feet)
Reference
Line : DA=25

100

Table 12: Light Shelf Combination Rank for 40 feet Depth Room
Rank
Light
Shelf
Height
(feet)
Light
Shelf
Width
(feet)
Light
Shelf
Curvature
Light
Shelf
Tilt
Angle
D
A
Rank
Light
Shelf
Height
(feet)
Light
Shelf
Width
(feet)
Light
Shelf
Curvature
Light
Shelf
Tilt
Angl
e
D
A
1 7 4 15 30 52 37 8 3 15 15 28
2 7 3 15 30 49 38 8 3 15 15 28
3 7 4 0 30 48 39 8 2 15 15 28
4 7 4 30 30 47 40 7 1 0 15 27
5 7 2 15 30 44 41 8 3 0 15 27
6 8 4 15 30 44 42 8 2 0 15 27
7 7 3 0 30 43 43 8 2 30 15 27
8 8 3 15 30 42 44 8 1 15 15 27
9 7 4 30 15 40 45 8 4 0 15 26
10 7 3 30 15 40 46 8 1 30 15 26
11 7 3 30 30 40 47 8 1 30 30 26
12 7 2 30 30 40 48 7 1 30 0 25
13 8 4 30 30 39 49 8 1 0 15 25
14 8 2 15 30 39 50 7 1 0 0 24
15 7 2 0 30 38 51 7 1 15 0 24
16 8 4 0 30 37 52 7 2 0 0 23
17 7 1 15 30 36 53 7 2 15 0 23
18 8 3 0 30 36 54 8 1 15 0 23
19 7 2 30 15 35 55 8 1 30 0 23
20 8 3 30 30 35 56 7 4 15 0 22
21 8 2 0 30 35 57 7 3 0 0 22
22 7 1 0 30 34 58 7 3 30 0 22
23 7 1 30 15 34 59 7 2 30 0 22
24 7 4 15 15 32 60 8 2 30 0 22
25 8 1 0 30 32 61 8 1 0 0 22
26 7 4 0 15 31 62 8 2 0 0 22
27 7 3 15 15 31 63 8 2 15 0 22
28 7 1 30 30 31 64 7 4 0 0 21
29 7 3 0 15 30 65 7 4 30 0 21
30 8 4 30 15 30 66 7 3 15 0 21
31 8 2 30 30 30 67 8 3 0 0 20
32 8 1 15 30 30 68 8 3 15 0 20
33 7 2 0 15 29 69 8 3 30 0 20
34 7 2 15 15 29 70 8 4 0 0 19
35 7 1 15 15 29 71 8 4 15 0 18
36 8 3 30 15 29 72 8 4 30 0 18

101

5.4 45 feet Depth Room
5.4.1 Light Shelf Height 7 feet

Figure 65: Diagram Shows Relationship Between Light Shelf Variables (Curvature and Tilt Angle) and
Daylight Autonomy at 5 Feet from the Back Wall of the Test Room: 45 feet Depth Room, 7 Feet Height
Light Shelf

For 45 feet depth room with 7 feet height light shelf and 10 feet height ceiling, light shelf
angle and curvature all affect DA at rear of the room. Best combination that has the
highest DA is 30 degree tilt angle and 15 degree curvature. Comparing these four
0
30
0
7
14
21
28
0
15
30
Light Shelf Angle
DA at 5' from back of
the wall
Light Shelf Curvature
7' High, 1' Depth Light Shelf
0
30
0
7
14
21
28
0
15
30
Light Shelf Angle
DA at 5' from back of
the wall
Light Shelf Curvature
7' High, 2' Depth Light Shelf
0
30
0
7
14
21
28
0
15
30
Light Shelf Angle
DA at 5' from back of
the wall
Light Shelf Curvature
7' High, 3' Depth Light Shelf
0
30
0
7
14
21
28
0
15
30
Light Shelf Angle

DA at 5' from back of
the wall
Light Shelf Curvature

7' High, 4' Depth Light Shelf

102

diagrams, we can see light shelf width also could affect DA at rear of the room, the
highest DA happened at four feet light shelf and 1 foot light shelf doesn’t have the yellow
color area which means the light shelf is highly recommended. Figure 66 gives the
further analysis of the effect of light shelf width.

Figure 66: Diagram Shows Relationship between Light Shelf Variable (Width) and Daylight Autonomy at
5 Feet from the Back Wall of the Test Room: 45 feet Depth Room, 7 Feet Height Light Shelf

For 45’ depth room and 7’ height light shelf, the DA baseline is 7, 4 feet width light shelf
has the highest DA value of 23, while best case of 1 foot light shelf has the DA of 11.
Also, light shelf width is one of the key factors that affect light shelf performance in this
case.

11
7
15
6
21
5
23
5
0
5
10
15
20
25
1 2 3 4
DA at 5' away from the back wall
Light Shelf Width (feet)
Reference Line:
DA=7

103

5.4.2 Light Shelf Height 8 feet

Figure 67: Diagram Shows Relationship Between Light Shelf Variables (Curvature and Tilt Angle) and
Daylight Autonomy at 5 Feet from the Back Wall of the Test Room: 45 feet Depth Room, 8 Feet Height
Light Shelf

For 45 depth room with 8’ high light shelf and 10’ ceiling, the improvement of using
light shelf is already not obvious. DA is still primarily decided by light shelf angle, DA
increases when light shelf tilt angle gets bigger. Light shelf curvature will also affect DA.
DA reaches the highest value when light shelf curvature is 15 degree and tilt angle is 30
degree. This also shows that flat horizontal light shelf will not function well for room in
0
15
30
0
7
14
21
28
0
15
30
Light Shelf Angle
Daylight Autonamy
Light Shelf Curvature
8' High, 1' Depth Light Shelf
0
15
30
0
7
14
21
28
0
15
30
Light Shelf Angle
Daylight Autonamy
Light Shelf Curvature
8' High, 2' Depth Light Shelf
0
15
30
0
7
14
21
28
0
15
30
Light Shelf Angle
Daylight Autonamy
Light Shelf Curvature
8' High, 3' Depth Light Shelf
0
15
30
0
7
14
21
28
0
15
30
Light Shelf Angle
Daylight Autonamy
Light Shelf Curvature
8' High,4' Depth Light Shelf

104

this depth. Comparing these four diagrams, we can see that light shelf width also could
affect DA at rear of the room; the highest DA happened at four feet light shelf and 1 foot
light shelf doesn’t have the red color area which means the light shelf is recommended.
Figure 68 gives the further analysis of the effect of light shelf width.

Figure 68: Diagram Shows Relationship between Light Shelf Variable (Width) and Daylight Autonomy at
5 Feet from the Back Wall of the Test Room: 45 feet Depth Room, 8 Feet Height Light Shelf

For 45’ depth room and 8’ height light shelf, the DA baseline is 7, 4 feet width light shelf
has the highest DA value of 18, while best case of 1 foot light shelf has the DA of 12.
Lowest DA of each light shelf width is very close to each other. Light shelf width is one
of the key factors that affect light shelf performance in this case.

12
5
14
3
14
2
18
2
0
5
10
15
20
25
1 2 3 4
DA at 5' away from the back wall
Light Shelf Width (feet)
Reference Line:
DA=7

105

Table 13: Light Shelf Combination Rank for 45 feet Depth Room
Rank
Light
Shelf
Height
(feet)
Light
Shelf
Width
(feet)
Light
Shelf
Curvature
Light
Shelf
Tilt
Angle
DA Rank
Light
Shelf
Height
(feet)
Light
Shelf
Width
(feet)
Light
Shelf
Curvature
Light
Shelf
Tilt
Angle
D
A
1 7 4 15 30 23 37 8 1 15 30 1
0 2 7 3 15 30 21 38 8 2 30 15 1
0 3 7 4 0 30 18 39 8 4 30 15 1
0 4 8 4 15 30 18 40 8 1 30 15 9
5 7 4 15 15 16 41 8 1 30 30 9
6 7 2 0 30 15 42 7 1 0 30 8
7 7 3 0 15 15 43 7 1 30 30 8
8 7 3 15 15 15 44 7 2 30 30 8
9 7 4 0 15 15 45 8 3 30 30 8
10 7 4 30 30 15 46 8 4 30 30 8
11 8 4 0 30 15 47 7 1 0 0 7
12 8 4 15 15 15 48 7 1 15 0 7
13 8 2 0 30 14 49 7 1 30 0 7
14 8 3 0 15 14 50 7 2 15 0 7
15 8 3 0 30 14 51 7 3 15 0 7
16 8 3 15 15 14 52 8 1 15 0 7
17 8 3 15 30 14 53 8 2 30 30 7
18 7 2 0 15 13 54 7 2 0 0 6
19 7 2 15 15 13 55 7 2 30 0 6
20 7 2 15 30 13 56 7 3 0 0 6
21 8 2 15 15 13 57 7 4 0 0 6
22 8 4 0 15 13 58 8 1 30 0 6
23 8 1 0 30 12 59 8 2 15 0 6
24 8 1 15 15 12 60 7 3 30 0 5
25 8 2 0 15 12 61 7 4 15 0 5
26 8 2 15 30 12 62 7 4 30 0 5
27 7 1 0 15 11 63 8 1 0 0 5
28 7 1 15 15 11 64 8 2 30 0 4
29 7 1 15 30 11 65 8 3 0 0 4
30 7 3 30 15 11 66 8 3 15 0 4
31 7 4 30 15 11 67 8 2 0 0 3
32 8 1 0 15 11 68 8 4 15 0 3
33 8 3 30 15 11 69 8 4 30 0 3
34 7 1 30 15 10 70 8 3 30 0 2
35 7 2 30 15 10 71 8 4 0 0 2
36 7 3 30 30 10 72 7 3 0 30 0

106

5.5 50 feet Depth Room
5.5.1 Light Shelf Height 7 feet

Figure 69: Diagram Shows Relationship Between Light Shelf Variables (Curvature and Tilt Angle) and
Daylight Autonomy at 5 Feet from the Back Wall of the Test Room: 50 feet Depth Room, 7 Feet Height
Light Shelf

For 50’ depth room and 7’ height light shelf, the improvement of using light shelf is even
smaller, which could only improve DA value to no bigger than 10. Light shelf curvature
and tilt angle will both affect DA. But light shelf tilt angle is not the bigger, the better as
0
30
0
3
6
9
0
15
30
Light Shelf Angle
Daylight Autonomy
Light Shelf Curvature
7' High, 1' Depth Light Shelf
0
30
0
3
6
9
0
15
30
Light Shelf Angle
Daylight Autonomy
Light Shelf Curvature
7' High, 2' Depth Light Shelf
0
30
0
3
6
9
0
15
30
Light Shelf Angle
Daylight Autonomy
Light Shelf Curvature
7' High, 3' Depth Light Shelf
0
30
0
3
6
9
0
15
30
Light Shelf Angle
Daylight Autonomy
Light Shelf Curvature
7' High, 4' Depth Light Shelf

107

it is in other rooms. For both width light shelf, DA has the highest value when curvature
is 15 and tilt angle is 15. This also shows that flat horizontal light shelf will not function
well for room in this depth. Comparing these four diagrams, we can see light shelf width
also could affect DA at rear of the room; the highest DA happened at four feet light shelf
and 1 foot light shelf doesn’t have the red color area which means the light shelf is
recommended. Figure 70 gives the further analysis of the effect of light shelf width.

Figure 70: Diagram Shows Relationship between Light Shelf Variable (Width) and Daylight Autonomy at
5 Feet from the Back Wall of the Test Room: 50 feet Depth Room, 7 Feet Height Light Shelf

For 50’ depth room and 7’ height light shelf, the DA baseline is 0, 4 feet width light shelf
has the highest DA value of 10, while best case of 1 foot light shelf has the DA of 4.
Lowest DA of each light shelf width is 0. Light shelf width is one of the key factors that
affect light shelf performance in this case.
10
8
7
4
0
2
4
6
8
10
12
1 2 3 4
DA at 5' away from the back wall
Light Shelf Width (feet)
Reference
Line: DA=0

108

5.5.2 Light Shelf Height 8 feet

Figure 71: Diagram Shows Relationship Between Light Shelf Variables (Curvature and Tilt Angle) and
Daylight Autonomy at 5 Feet from the Back Wall of the Test Room: 50 feet Depth Room, 8 Feet Height
Light Shelf

For 50’ depth room and 8’ height light shelf, the improvement of using light shelf is even
smaller, which could only improve DA value to no bigger than 9. Light shelf curvature
and tilt angle will both affect DA. But light shelf tilt angle is not the bigger, the better as
it is in other rooms. For both width light shelf, DA has the highest value when curvature
is 15 and tilt angle is 15. This also shows that flat horizontal light shelf will not function
0
15
30
0
3
6
9
0
15
30
Light Shelf Angle
Daylight Autonomy
Light Shelf Curvature
8' High, 1' Depth Light Shelf
0
15
30
0
3
6
9
0
15
30
Light Shelf Angle
Daylight Autonomy
Light Shelf Curvature
8' High, 2' Depth Light Shelf
0
30
0
3
6
9
0
15
30
Light Shelf Angle
Daylight Autonomy
Light Shelf Curvature
8' High, 3' Depth Light Shelf
0
30
0
3
6
9
0
15
30
Light Shelf Angle
Daylight Autonomy
Light Shelf Curvature
8' High, 4' Depth Light Shelf

109

well for room in this depth. Comparing these four diagrams, we can see light shelf width
also could affect DA at rear of the room; the highest DA happened at four feet light shelf
and 1 foot light shelf doesn’t have the red color area which means the light shelf is
recommended. Figure 72 gives the further analysis of the effect of light shelf width.

Figure 72: Diagram Shows Relationship between Light Shelf Variable (Width) and Daylight Autonomy at
5 Feet from the Back Wall of the Test Room: 50 feet Depth Room, 8 Feet Height Light Shelf

For 50’ depth room and 8’ height light shelf, the DA baseline is 0, 4 feet width light shelf
has the highest DA value of 9, while the best case of 1 foot light shelf has the DA of 5.
Lowest DA of each light shelf width is 0. Light shelf width is one of the key factors that
affect light shelf performance in this case.

5
0 0
6
0
8
9
0
2
4
6
8
10
12
1 2 3 4
DA at 5' away from the back wall
Light Shelf Width (feet)
Reference
Line: DA=0

110

Table 14: Light Shelf Combination Rank for 50 feet Depth Room
Rank
Light
Shelf
Height
(feet)
Light
Shelf
Width(
feet)
Light
Shelf
Curvature
Light
Shelf
Tilt
Angle
DA Rank
Light
Shelf
Height
(feet)
Light
Shelf
Width(
feet)
Light
Shelf
Curvatu
re
Light
Shelf
Tilt
Angle
D
A
1 7 4 15 15 10 37 7 3 30 30 1
2 8 4 15 15 9 38 8 4 0 0 0
3 7 4 15 30 9 39 8 4 15 0 0
4 8 3 15 30 8 40 8 4 30 0 0
5 8 3 15 15 8 41 8 3 0 0 0
6 7 3 15 15 8 42 8 3 15 0 0
7 7 4 0 15 8 43 8 3 30 0 0
8 8 4 0 15 7 44 8 2 0 0 0
9 8 3 0 15 7 45 8 2 15 0 0
10 7 2 15 15 7 46 8 2 30 15 0
11 7 3 0 15 7 47 8 2 30 0 0
12 8 4 0 30 6 48 8 1 0 30 0
13 8 2 0 15 6 49 8 1 0 0 0
14 8 2 15 30 6 50 8 1 15 30 0
15 8 2 15 15 6 51 8 1 15 0 0
16 7 2 0 15 6 52 8 1 30 15 0
17 7 4 0 30 6 53 8 1 30 30 0
18 8 4 15 30 5 54 8 1 30 0 0
19 8 3 0 30 5 55 7 1 0 30 0
20 8 1 0 15 5 56 7 1 0 0 0
21 7 3 0 30 5 57 7 1 15 30 0
22 8 4 30 15 4 58 7 1 15 0 0
23 8 4 30 30 4 59 7 1 30 15 0
24 7 1 0 15 4 60 7 1 30 30 0
25 7 1 15 15 4 61 7 1 30 0 0
26 7 2 15 30 4 62 7 2 0 0 0
27 7 3 15 30 4 63 7 2 15 0 0
28 8 2 0 30 3 64 7 2 30 15 0
29 7 2 0 30 2 65 7 2 30 30 0
30 8 3 30 30 1 66 7 2 30 0 0
31 8 3 30 15 1 67 7 3 0 0 0
32 8 2 30 30 1 68 7 3 15 0 0
33 8 1 15 15 1 69 7 3 30 0 0
34 7 3 30 15 1 70 7 4 0 0 0
35 7 4 30 30 1 71 7 4 15 0 0
36 7 4 30 15 1 72 7 4 30 0 0

111

5.6 Light Shelf Variables Tendency Analysis
5.6.1 Light Shelf Width Variable Analysis

Figure 73: Visual Presentation of Light Shelf Width Variable in This Study

Figure 74: Performance Curve Represent Relationship between Light Shelf Width and DA at rear of the
room

30
40
50
60
70
80
1 2 3 4
DA at 5' away from the back
wall
Light Shelf Width
35' Depth Room
0
10
20
30
40
50
60
1 2 3 4
DA at 5' away from the back
wall
Light Shelf Width
40' Depth Room
0
10
20
30
40
50
1 2 3 4
DA at 5' away from the back
wall
Light Shelf Width
45' Depth Room
0
10
20
30
40
50
1 2 3 4
DA at 5' away from the back
wall
Light Shelf Width
50' Depth Room

112

From Figure 74 we know, for rooms from 35’ to 50’ depth, the increase of the light shelf
width has a positive impact on room daylight penetration depth. However, light shelf
width is not a key factor in improvig light shelf performance.

113

5.6.2 Light Shelf Curvature Variable Analysis

Figure 75: Visual Presentation of Light Shelf Curvature Variable in This Study

Figure 76: Performance Curve Represent Relationship between Light Shelf Curvature and DA at rear of
the room

The impact of light shelf curvature on tested DA value of the room is relatively complex.
For 35’ depth and 40’ depth room, there is not clear relationship between light shelf
30
40
50
60
70
80
0 15 30
DA at 5' away from the back
wall
Light Shelf Curvature
35' Depth Room
0
10
20
30
40
50
60
0 15 30
DA at 5' away from the back
wall
Light Shelf Curvature
40' Depth Room
0
10
20
30
40
50
0 15 30
DA at 5' away from the back
wall
Light Shelf Curvature
45' Depth Room
0
2
4
6
8
10
12
14
0 15 30
DA at 5' away from the back
wall
Light Shelf Curvature
50' Depth Room

114

curvature and DA. For 45’ depth room and 50’ depth room, curvature of 15 degree has
the most positive affect on DA improvement in range of 0 to 30 degree. It may be that if
the curved shelf were tipped inward, the impact would be more significant. This would
be worth further study.

115

5.6.3 Light Shelf Tilt Angle Variable Analysis

Figure 77: Visual Presentation of Light Shelf Tilt Angle Variable in This Study

Figure 78: Performance Curve Represent Relationship between Light Shelf Tilt Angle and DA at rear of
the room

Among all four variables, tilt angle has the most significant impact on DA at rear of the
room. For 35’,40’ and 45’ depth room, the bigger the light shelf angle the bigger the DA.
30
40
50
60
70
80
0 15 30 DA at 5' away from the back
wall
Light Shelf Angle
35' Depth Room
0
10
20
30
40
50
60
0 15 30
DA at 5' away from the back
wall
Light Shelf Angle
40' Depth Room
0
10
20
30
40
50
0 15 30
DA at 5' away from the back
wall
Light Shelf Angle
45' Depth Room
0
2
4
6
8
10
12
14
0 15 30
DA at 5' away from the back
wall
Light Shelf Angle
50' Depth Room

116

But when room is 50’ depth, the relationship between light shelf angle and DA is not that
simple. 15 degree tilt angle has the most positive impact on the increase of DA.

117

5.6.4 Light Shelf Height Variable Analysis

Figure 79: Visual Presentation of Light Shelf Height Variable in This Study

Figure 80: Performance Curve Represent Relationship between Light Shelf Height and DA at rear of the
room

30
40
50
60
70
80
7 8
DA at 5' away from the back
wall
Light Shelf Height
35' Depth Room
0
10
20
30
40
50
7 8
DA at 5' away from the back
wall
Light Shelf Height
40' Depth Room
0
10
20
30
40
50
7 8
DA at 5' away from the back
wall
Light Shelf Height
45' Depth Room
0
10
20
30
40
50
7 8
DA at 5' away from the back
wall
Light Shelf Height
50' Depth Room

118

In this study, light shelf height only has two variables, 7 feet and 8 feet. For 35’, 40’ and
45’ depth room, 7’ height light shelf has a better performance than 8’ light shelf. For 50’
depth room, there is no clear advantage for each height light shelf.

119

Chapter 6 Light Shelf Design Assistant Tools: Design Guideline and
Quick Calculation Equations
Because there are many variables that could affect light shelf performance, it is hard for
architects and consultant to design an efficient light shelf. Create light shelf design
assistant tools that help architects and consultants to figure out the appropriate light shelf
configurations when they design a light shelf are the final goal of this study. The
workflow used in this study could be used to get a precise result, but as the simulation
process is time consuming, some quick calculation tools are needed. In this chapter, two
quick calculation tools based on the data we get from the previous simulation will be
introduced, light shelf design guideline and quick calculation equations.

120

6.1 Light Shelf Design Assistant Tools
We could learn from the Chapter 5 that there are many variables affect light shelf
performance, and all the variables will not affect light shelf performance independently.
Moreover, each variable’s affect is hard to simply explain. These all add to difficulty for
architects and consultants to design and select an appropriate configuration light shelf.
Create light shelf design assistant tools that help architects and consultants to figure out
the appropriate light shelf configurations when they design a light shelf are the final goal
of this study. The workflow used in this study could be used to get a precise result, but as
the simulation process is pretty time consuming, some quick calculation tools are
preferred. In this chapter, two quick calculation tools based on the data we get from the
previous simulation will be introduced, light shelf design guideline and quick calculation
equations.
6.2 Light Shelf Design Guidelines
Light shelf design guidelines is a simple tool that created based on the simulation results
and analysis presented in Chapter 5. This guideline will be presented in graphic way
which easy for architects to understand. The guideline includes four pages; each page
includes guideline for one depth room from 35’ to 50’. Users could refer to appropriate
room depth page and be informed how to select the appropriate light shelf that is suitable
for such depth room. For each depth room, 8 diagrams are presented categorized by light

121

shelf height and light shelf width. Each diagram represents the relationship between
Daylight Autonomy and light shelf curvature and tilt angle.
The horizontal axis represents the light shelf curvature, which ranges from 0 to 30 degree
while the vertical axis on the right represents the light shelf tilt angle, which also ranges
from 0 to 30 degree. DA is represented by color; the value range of each color could be
seen in legend at the right.
Baseline DA which represents the DA of the reference room without light shelf is noted
at the top of the guideline. And the DA range that is higher than the baseline DA is also
red clouded in the legend for users to easily compare.

122

6.2.1 35’ Depth Room Light Shelf Design Guideline (baseline DA=45)

0
15
30
0 15 30
7' High, 1' Depth Light Shelf
0
15
30
0 15 30
8' High, 1' Depth Light Shelf
0
15
30
0 15 30
7' High, 2' Depth Light Shelf
0
15
30
0 15 30
8' High, 2' Depth Light Shelf
0
15
30
0 15 30
7' High, 3' Depth Light Shelf
0
15
30
0 15 30
8' High, 3' Depth Light Shelf
0
15
30
0 15 30
7' High, 4' Depth Light Shelf
0
15
30
0 15 30
8' High, 4' Depth Light Shelf

123

6.2.2 40’ Depth Room Light Shelf Design Guideline (baseline DA=25)

0
15
30
0 15 30
7' Height, 1' Depth Light Shelf
0
15
30
0 15 30
8' Height, 1' Depth Light Shelf
0
15
30
0 15 30
7' Height, 2' Depth Light Shelf
0
15
30
0 15 30
8' Height, 2' Depth Light Shelf
0
15
30
0 15 30
7' Height, 3' Depth Light Shelf
0
15
30
0 15 30
8' Height, 3' Depth Light Shelf
0
15
30
0 15 30
7' Height, 4' Depth Light Shelf
0
15
30
0 15 30
8' Height, 4' Depth Light Shelf

124

6.2.3 45’ Depth Room Light Shelf Design Guideline (baseline DA=7)

0
15
30
0 15 30
7' High, 1' Depth Light Shelf
0
15
30
0 15 30
8' High, 1' Depth Light Shelf
0
15
30
0 15 30
7' High, 2' Depth Light Shelf
0
15
30
0 15 30
8' High, 2' Depth Light Shelf
0
15
30
0 15 30
7' High, 3' Depth Light Shelf
0
15
30
0 15 30
8' High, 3' Depth Light Shelf
0
15
30
0 15 30
7' High, 4' Depth Light Shelf
0
15
30
0 15 30
8' High,4' Depth Light Shelf

125

6.2.4 50’ Depth Room Light Shelf Design Guideline (baseline DA=0)

0
15
30
0 15 30
7' High, 1' Depth Light Shelf
0
15
30
0 15 30
8' High, 1' Depth Light Shelf
0
15
30
0 15 30
7' High, 2' Depth Light Shelf
0
15
30
0 15 30
8' High, 2' Depth Light Shelf
0
15
30
0 15 30
7' High, 3' Depth Light Shelf
0
15
30
0 15 30
8' High, 3' Depth Light Shelf
0
15
30
0 15 30
7' High, 4' Depth Light Shelf
0
15
30
0 15 30
8' High, 4' Depth Light Shelf

126

6.3 Quick Calculation Equations
Because running a DIVA simulation process is a time consuming process, more quick
tools are necessary to give architects and consultants a quick answer that whether or not
the light shelf is good for a particular depth room. Diagram guideline is a good way to
show this but if they need a more precise number, a quick calculation equation should be
used.
Quick calculation equations are developed to reflect a three-dimensional relationship
between input variables (light shelf width, light shelf curvature and light shelf tilt angle)
and output results (Daylight Autonomy value of the sensor at 5’ away from the room
back wall).
Room depth and light shelf height are not involved in input variables to make the
equation. So there will be totally 8 equations to include all 4 room depth and 2 light shelf
height situation.
All equations will be created based on the data collected from the previous simulation by
DIVA, because the large size of the sample data, the results could be relatively precise.
Excel is selected as the tool to create the quick calculation equation.
According to EnergyPlus Engineering Reference page 1245 (Laboratory 2011), the
equations that include degree of 2 in two independent variables and degree of 1 in
another one independent variable should be in following format.

127

Equation 2: Sample Equation

Output=Daylight Autonomy at the Point 5’ from the Room Back Wall
x= 2 degree variable
y=2 degree variable
z= 1 degree variable
However, multivariate regression analysis of Excel only allows for 16 variables while in
this equation there are total 17 variables. After cautious selection and making sure the
prediction is within 15% deviation, only 16 variables will be included in final equation.
For different depths of room, the variables and equation will be different, but the analysis
process will be similar, so 35’ depth room will be used as an example with detail
explanation, and the 40’, 45’, and 50’ depth room will just show the data and short
description with the final results, no detail process will be explained.
6.3.1. 35’Depth Room, 7’ Height Light Shelf
Regression Analysis of Excel is used to create the prediction equation. First, the degree of
each light shelf independent variable needs to be tested and confirmed. Then which 16
out of 17 variables should be included in final equation need to be tested and confirmed.

128

The selection process is time-consuming, based on lots of tests, and not especially related
with the final results, so they will be neglected in this chapter.
Calculating performance curve coefficients in a spreadsheet is a simple matter of finding
the data required to perform the regression analysis.
Given the data set shown in the table below, each of the independent variables would be
calculated according to the fundamental equation mentioned before. The fundamental
equation would be used to determine the number of independent variables and also the
form of the equation. Given the example described here, the spreadsheet would be set up
to look like the equation as shown in the following table. A regression analysis could then
be performed on the data set. The first 16 columns are the independent variables.
And the last column is the dependent variable. A spreadsheet tool is selected to perform
the regression analysis, and the coefficients are calculated and displayed in the
spreadsheet. The spreadsheet sample is just a part of the whole spreadsheet; the data is
not completed presented.
Table 15: Sample of Excel Spreadsheet to Conduct Regression Analysis
X X² Y² Y Z x² y² xy xy² x² y xz x² z yz y² z x² y² z x² yz xyz xy² z OUTPUT
1 1 0 0 45 0 0 0 0 45 45 0 0 0 0 0 0 66
1 1 0 0 30 0 0 0 0 30 30 0 0 0 0 0 0 64
1 1 225 15 30 225 15 225 15 30 30 450 6750 6750 450 450 6750 64
1 1 900 30 30 900 30 900 30 30 30 900 27000 27000 900 900 27000 64
1 1 900 30 15 900 30 900 30 15 15 450 13500 13500 450 450 13500 61
1 1 225 15 15 225 15 225 15 15 15 225 3375 3375 225 225 3375 57
1 1 0 0 15 0 0 0 0 15 15 0 0 0 0 0 0 55
1 1 225 15 0 225 15 225 15 0 0 0 0 0 0 0 0 49
1 1 900 30 0 900 30 900 30 0 0 0 0 0 0 0 0 46
1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 45

129

2 4 0 0 45 0 0 0 0 90 180 0 0 0 0 0 0 71
2 4 225 15 30 900 30 450 60 60 120 450 6750 27000 1800 900 13500 71
2 4 900 30 30 3600 60 1800 120 60 120 900 27000 108000 3600 1800 54000 71
2 4 0 0 30 0 0 0 0 60 120 0 0 0 0 0 0 70
2 4 225 15 15 900 30 450 60 30 60 225 3375 13500 900 450 6750 66
2 4 0 0 15 0 0 0 0 30 60 0 0 0 0 0 0 65
2 4 900 30 15 3600 60 1800 120 30 60 450 13500 54000 1800 900 27000 65
2 4 900 30 0 3600 60 1800 120 0 0 0 0 0 0 0 0 46
2 4 225 15 0 900 30 450 60 0 0 0 0 0 0 0 0 45
2 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 42
3 9 0 0 30 0 0 0 0 90 270 0 0 0 0 0 0 74
3 9 225 15 30 2025 45 675 135 90 270 450 6750 60750 4050 1350 20250 74
3 9 900 30 30 8100 90 2700 270 90 270 900 27000 243000 8100 2700 81000 74
3 9 0 0 45 0 0 0 0 135 405 0 0 0 0 0 0 73
…
The regression analysis and summary statistical output is shown below. The equation
coefficients are shown highlighted. In this example, the equation coefficients are: a =
44.01123, b = 3.017043, c= -0.35718, d = -0.00734, e = 0.490159, f = 0.280056, g =
0.00448, h = -0.20809, i = -0.00342, j = -0.04735, k = 0.235354, l = -0.0369, m = -
0.01306, n = 0.00018, o = -0.00018, p = 0.001362, q = -0.015525. These coefficients
would be entered in an equation to describe the relationship between light shelf
configuration and DA at rear of the room.

Table 16: Excel Regression Analysis Report: 35’ Depth Room and 7’ Height Light Shelf
SUMMARY OUTPUT

Regression Statistics

Multiple R 0.922659

R Square 0.851299

Adjusted R
Square
0.738003

Standard
Error
5.851633

Observations 38

130

ANOVA

df SS MS F Significanc
e F

Regression 16 4116.637 257.28
98
7.5139529
84
1.84E-05

Residual 21 719.0737 34.241
6

Total 37 4835.711

Coefficients Standard
Error
t Stat P-value Lower 95% Upper
95% Intercept 44.01123 13.35296 3.2959
91
0.0034418
9
16.24224 71.7802
3 X Variable 1 3.017043 12.15689 0.2481
76
0.8064092
53
-22.2646 28.2986
8 X Variable 2 -0.35718 2.395094 -
0.1491
3
0.8828744
45
-5.33805 4.62369
3 X Variable 3 -0.00734 0.054209 -
0.1353
7
0.8936114
44
-0.12007 0.10539
6 X Variable 4 0.490159 1.7768 0.2758
66
0.7853472
94
-3.2049 4.18521
8 X Variable 5 0.280056 0.470268 0.5955
24
0.5578571
66
-0.69792 1.25803
3 X Variable 6 0.00448 0.009825 0.4560
04
0.6530675
86
-0.01595 0.02491
1 X Variable 7 -0.20809 1.541977 -
0.1349
5
0.8939347
98
-3.41481 2.99862
3 X Variable 8 -0.00342 0.047205 -
0.0724
1
0.9429573
31
-0.10159 0.09475
X Variable 9 -0.04735 0.309213 -
0.1531
3
0.8797592
49
-0.69039 0.59569
4 X Variable 10 0.235354 0.427627 0.5503
71
0.5878719
29
-0.65395 1.12465
3 X Variable 11 -0.0369 0.084285 -
0.4378
4
0.6659740
27
-0.21218 0.13837
7 X Variable 12 -0.01306 0.047711 -
0.2737
9
0.7869208
49
-0.11228 0.08615
7 X Variable 13 0.00018 0.001201 0.1502
4
0.8820091
86
-0.00232 0.00267
8 X Variable 14 -0.00018 0.000143 -
1.2599
9
0.2214960
14
-0.00048 0.00011
8 X Variable 15 0.001362 0.006749 0.2017
72
0.8420364
67
-0.01267 0.01539
7 X Variable 16 0.015525 0.030021 0.5171
46
0.6104586
67
-0.04691 0.07795
7

Before the coefficient of each variable is confirmed, a test of the results accuracy is
performed. The preferred deviation is within 15%. The diagram below shows the
comparison between simulation DA and predicted DA.

30
40
50
60
70
80
90
30 40 50 60 70 80
DA(Simulation)
DA(predicted)

131

Figure 81: Measured DA versus Predicted DA: 35’ Depth Room and 7’ Height Light Shelf

After all these steps, a quick calculation equation of 35’room depth and 7’ light shelf
height is created and presented as below. The process for the following depth room are
similar with this sample, so the following parts will only presented the data and final
equations, not detail process will be explained.

Equation 3: DA Prediction for 35’ Depth Room with 7’ Height Light Shelf

x= Light Shelf Width
y=Light Shelf Curvature
z= Light Shelf Tilt Angle

132

6.3.2. 35’Depth Room, 8’ Height Light Shelf

Table 17: Excel Regression Analysis Report: 35’ Depth Room and 8’ Height Light Shelf
SUMMARY OUTPUT

Regression Statistics

Multiple R 0.983585

R Square 0.96744

Adjusted R
Square
0.942632

Standard Error 2.711921

Observations 38

ANOVA

df SS MS F Significanc
e F

Regression 16 4588.924 286.80
77
38.997504
56
4.89E-12

Residual 21 154.4448 7.3545
15

Total 37 4743.368

Coefficients Standard
Error
t Stat P-value Lower 95% Upper
95% Intercept 45.62754 6.188386 7.3730
91
2.96981E-
07
32.75808 58.4969
9 X Variable 1 -1.73965 5.634072 -
0.3087
7
0.7605367
57
-13.4563 9.97704
6 X Variable 2 0.132878 1.109999 0.1197
1
0.9058510
74
-2.17549 2.44124
7 X Variable 3 0.01274 0.025123 0.5071
21
0.6173542
51
-0.03951 0.06498
7 X Variable 4 -0.22795 0.823453 -
0.2768
2
0.7846223
16
-1.94041 1.48451
3 X Variable 5 0.280443 0.217944 1.2867
63
0.2121813
89
-0.1728 0.73368
3 X Variable 6 0.00521 0.004553 1.1442
51
0.2653949
56
-0.00426 0.01467
9 X Variable 7 0.219798 0.714624 0.3075
72
0.7614379
82
-1.26634 1.70594
1 X Variable 8 -0.01196 0.021877 -
0.5468
6
0.5902373
47
-0.05746 0.03353
2 X Variable 9 -0.10543 0.143304 -
0.7356
8
0.4700647
68
-0.40344 0.19259
1 X Variable 10 0.241207 0.198182 1.2170
94
0.2370699
26
-0.17094 0.65334
9 X Variable 11 -0.03091 0.039062 -
0.7912
0.4376708
85
-0.11214 0.05032
7 X Variable 12 0.004597 0.022111 0.2079
23
0.8372925
35
-0.04139 0.05058
1 X Variable 13 -0.00034 0.000557 -
0.6117
3
0.5472832
06
-0.0015 0.00081
7 X Variable 14 -0.00012 6.65E-05 -
1.7456
6
0.0954857
18
-0.00025 2.22E-
05 X Variable 15 0.001326 0.003128 0.4238
07
0.6760158
56
-0.00518 0.00783
X Variable 16 0.008962 0.013913 0.6441
27
0.5264663
86
-0.01997 0.03789
6

133

Figure 82: Measured DA versus Predicted DA: 35’ Depth Room and 8’ Height Light Shelf

Equation 4: DA Prediction for 35’ Depth Room with 8’ Height Light Shelf
Output=45.62754-1.73965x+0.132878x² +0.01274y² -
0.22795y+0.280443z+0.00521x² y² +0.219798xy-0.01196xy² -0.10543x²
y+0.241207xz-0.03091x² z+0.004597yz-0.00034y² z-
0.00012x² y² z+0.001326x² yz+0.008962xyz
x= Light Shelf Width
y=Light Shelf Curvature
z= Light Shelf Tilt Angle

30
35
40
45
50
55
60
65
70
75
80
30 40 50 60 70 80
DA(Simulation)
DA(predicted)

134

6.3.3. 40’Depth Room, 7’ Height Light Shelf
Table 18: Excel Regression Analysis Report: 40’ Depth Room and 7’ Height Light Shelf
SUMMARY OUTPUT

Regression Statistics

Multiple R 0.969856

R Square 0.94062

Adjusted R
Square
0.914942

Standard
Error
2.964178

Observations 54

ANOVA

df SS MS F Significanc
e F

Regression 16 5149.738 321.85
86
36.631658
93
7.71E-18

Residual 37 325.095 8.7863
52

Total 53 5474.833

Coefficients Standard
Error
t Stat P-value Lower 95% Upper
95% Intercept 24.86898 2.683125 9.2686
61
3.48735E-
11
19.43245 30.3055
1 X Variable 1 -1.85093 2.86235 -
0.6466
5
0.5218512
19
-7.6506 3.94873
9 X Variable 2 0.150378 0.648798 0.2317
79
0.8179870
57
-1.16421 1.46496
8 X Variable 3 0.011394 0.020862 0.5461
62
0.5882331
39
-0.03088 0.05366
3 X Variable 4 -0.26584 0.65978 -
0.4029
2
0.6893279
77
-1.60268 1.07100
4 X Variable 5 0.076363 0.231642 0.3296
6
0.7435157
5
-0.39299 0.54571
5 X Variable 6 0.001912 0.002868 0.6668
77
0.5089882
82
-0.0039 0.00772
3 X Variable 7 0.350584 0.548528 0.6391
35
0.5266723
81
-0.76084 1.46200
7 X Variable 8 -0.01134 0.015865 -
0.7145
4
0.4793787
23
-0.04348 0.02081
X Variable 9 -0.06328 0.106129 -
0.5962
5
0.5546376
13
-0.27832 0.15175
8 X Variable 10 0.256635 0.212817 1.2058
99
0.2355115
78
-0.17457 0.68784
3 X Variable 11 -0.01287 0.044449 -
0.2895
3
0.7737958
3
-0.10293 0.07719
3 X Variable 12 0.0056 0.018494 0.3028
14
0.7637279
58
-0.03187 0.04307
3 X Variable 13 -0.00051 0.000432 -
1.1721
9
0.2486123
58
-0.00138 0.00036
9 X Variable 14 2.4E-05 4.41E-05 0.5432
33
0.5902273
68
-6.5E-05 0.00011
3 X Variable 15 -0.0021 0.003123 -
0.6728
2
0.5052414
28
-0.00843 0.00422
6 X Variable 16 0.008497 0.013046 0.6513
48
0.5188471
93
-0.01794 0.03493
1

135

Figure 83: Measured DA versus Predicted DA: 40’ Depth Room and 7’ Height Light Shelf

Equation 5: DA Prediction for 40’ Depth Room with 7’ Height Light Shelf

( )

x= Light Shelf Width
y=Light Shelf Curvature
z= Light Shelf Tilt Angle

10
15
20
25
30
35
40
45
50
55
60
10 20 30 40 50 60
DA(Simulation)
DA(predicted)

136

6.3.4. 40’Depth Room, 8’ Height Light Shelf

Table 19: Excel Regression Analysis Report: 40’ Depth Room and 8’ Height Light Shelf
SUMMARY OUTPUT

Regression Statistics

Multiple R 0.990285

R Square 0.980665

Adjusted R
Square
0.96829

Standard Error 1.26177

Observations 42

ANOVA

df SS MS F Significanc
e F

Regression 16 2018.675 126.16
72
79.247573
39
2.1E-17

Residual 25 39.80159 1.5920
63

Total 41 2058.476

Coefficien
ts
Standard
Error
t Stat P-value Lower 95% Upper
95% Intercept 22.74096 2.712233 8.3845
88
9.87765E-
09
17.15501 28.3269
X Variable 1 -0.56251 2.2278 -
0.2524
9
0.8027229
49
-5.15075 4.02573
2 X Variable 2 -0.12699 0.422517 -
0.3005
5
0.7662423
64
-0.99718 0.74320
2 X Variable 3 0.012233 0.011404 1.0727
14
0.2936454
76
-0.01125 0.03571
9 X Variable 4 -0.24701 0.365586 -
0.6756
6
0.5054619
59
-0.99995 0.50592
9 X Variable 5 0.093549 0.144249 0.6485
27
0.5225571
75
-0.20354 0.39063
6 X Variable 6 0.002697 0.002062 1.3083
45
0.2026580
69
-0.00155 0.00694
3 X Variable 7 0.279118 0.317401 0.8793
87
0.3875662
03
-0.37458 0.93281
7 X Variable 8 -0.01148 0.010053 -
1.1417
6
0.2643737
2
-0.03218 0.00922
7 X Variable 9 -0.0715 0.064316 -
1.1116
5
0.2768672
54
-0.20396 0.06096
4 X Variable 10 0.231744 0.124182 1.8661
56
0.0737937
81
-0.02401 0.48750
2 X Variable 11 -0.02818 0.024079 -
1.1702
4
0.2529384
65
-0.07777 0.02141
4 X Variable 12 0.00438 0.011523 0.3800
85
0.7070922
04
-0.01935 0.02811
2 X Variable 13 -0.00048 0.000286 -
1.6739
5
0.1066086
03
-0.00107 0.00011
X Variable 14 -4.5E-05 2.87E-05 -
1.5688
6
0.1292516
05
-0.0001 1.41E-
05 X Variable 15 0.001761 0.001545 1.1396
12
0.2652494
43
-0.00142 0.00494
3 X Variable 16 0.001837 0.006693 0.2745
06
0.7859514
74
-0.01195 0.01562
2

137

Figure 84: Measured DA versus Predicted DA: 40’ Depth Room and 8’ Height Light Shelf

Equation 6: DA Prediction for 40’ Depth Room with 8’ Height Light Shelf

( )
x= Light Shelf Width
y=Light Shelf Curvature
z= Light Shelf Tilt Angle

10
15
20
25
30
35
40
45
50
55
60
10 20 30 40 50 60
DA(Simulation)
DA(predicted)

138

6.3.5. 45’Depth Room, 7’ Height Light Shelf

Table 20: Excel Regression Analysis Report: 45’ Depth Room and 7’ Height Light Shelf
SUMMARY OUTPUT

Regression
Statistics

Multiple R 0.979602

R Square 0.959621

Adjusted R
Square
0.944937

Standard Error 0.99785

Observations 61

ANOVA

df SS MS F Significa
nce F

Regression 16 1041.173 65.0732
9
65.354033
36
2.57E-25

Residual 44 43.81099 0.99570
4

Total 60 1084.984

Coefficients Standard
Error
t Stat P-value Lower 95% Upper
95% Intercept 7.195074 1.178685 6.10432
3
2.37062E-
07
4.819591 9.5705
57 X Variable 1 -0.37803 0.427153 -0.885 0.3809683
64
-1.2389 0.4828
4 X Variable 2 -0.01359 0.004205 -
3.23237
0.0023285
64
-0.02207 -
0.0051
2
X Variable 3 -0.00182 0.00519 -
0.35122
0.7270993
25
-0.01228 0.0086
36 X Variable 4 0.071346 0.166003 0.42979
1
0.6694451
91
-0.26321 0.4059
03 X Variable 5 0.393415 0.145252 2.7085 0.0095915
54
0.100679 0.6861
5 X Variable 6 2.12E-05 1.37E-05 1.54702
7
0.1290198
85
-6.4E-06 4.88E-
05 X Variable 7 0.010392 0.013275 0.78280
1
0.4379367
59
-0.01636 0.0371
47 X Variable 8 -0.00044 0.000362 -
1.21919
0.2292666
63
-0.00117 0.0002
88 X Variable 9 -0.00064 0.000455 -
1.40778
0.1662215
26
-0.00156 0.0002
77 X Variable 10 0.123523 0.05184 2.38277
5
0.0215676
52
0.019046 0.228
X Variable 11 -0.00045 0.001477 -
0.30308
0.7632597
11
-0.00342 0.0025
29 X Variable 12 -0.01508 0.054824 -
0.27507
0.7845509
68
-0.12557 0.0954
11 X Variable 13 5.82E-05 0.001688 0.03450
9
0.9726273
61
-0.00334 0.0034
59 X Variable 14 -1E-05 3.34E-06 -3.0872 0.0034912
53
-1.7E-05 -3.6E-
06 X Variable 15 0.000364 0.000125 2.90622
8
0.0057079
13
0.000112 0.0006
16 X Variable 16 -0.00192 0.002909 -
0.65908
0.5132813
24
-0.00778 0.0039
45

139

Figure 85: Measured DA versus Predicted DA: 45’ Depth Room and 7’ Height Light Shelf

Equation 7: DA Prediction for 45’ Depth Room with 7’ Height Light Shelf

( )

( )

( )

x= Light Shelf Width
y=Light Shelf Curvature
z= Light Shelf Tilt Angle

0.0
5.0
10.0
15.0
20.0
25.0
0 5 10 15 20 25
DA (simulation)
DA (Predicted)

140

6.3.6. 45’Depth Room, 8’ Height Light Shelf

Table 21: Excel Regression Analysis Report: 45’ Depth Room and 8’ Height Light Shelf
SUMMARY OUTPUT

Regression Statistics

Multiple R 0.99111

R Square 0.982298

Adjusted R
Square
0.974644

Standard Error 0.633467

Observations 54

ANOVA

df SS MS F Significanc
e F

Regression 16 823.9119 51.494
49
128.32561
14
1.94E-27

Residual 37 14.84736 0.4012
8

Total 53 838.7593

Coefficients Standard
Error
t Stat P-value Lower 95% Upper
95% Intercept 6.417398 0.484265 13.251
84
1.27493E-
15
5.436185 7.39861
1 X Variable 1 -1.1087 0.196377 -
5.6457
6
1.89552E-
06
-1.5066 -0.7108
X Variable 2 -0.00536 0.002553 -
2.0980
5
0.0427877
32
-0.01053 -
0.00018 X Variable 3 -0.00859 0.003228 -
2.6607
1
0.0114631
79
-0.01513 -
0.00205 X Variable 4 0.261878 0.096216 2.7217
83
0.0098412
56
0.066927 0.45683
X Variable 5 0.351214 0.077056 4.5578
87
5.47776E-
05
0.195083 0.50734
5 X Variable 6 4.12E-05 9.3E-06 4.4326
39
8.00993E-
05
2.24E-05 6.01E-
05 X Variable 7 0.010223 0.008222 1.2434
67
0.2215171
55
-0.00644 0.02688
2 X Variable 8 -0.00045 0.000245 -
1.8527
1
0.0719134
73
-0.00095 4.25E-
05 X Variable 9 -0.00126 0.000303 -
4.1668
7
0.0001778
92
-0.00188 -
0.00065 X Variable 10 0.181509 0.029399 6.1739
29
3.65182E-
07
0.121941 0.24107
8 X Variable 11 -0.00399 0.000956 -4.173 0.0001746
74
-0.00593 -
0.00205 X Variable 12 -0.03391 0.033925 -
0.9995
8
0.3240050
72
-0.10265 0.03482
7 X Variable 13 0.001121 0.001116 1.0042
71
0.3217710
15
-0.00114 0.00338
2 X Variable 14 -1.3E-05 2.22E-06 -
5.7609
7
1.32328E-
06
-1.7E-05 -8.3E-
06 X Variable 15 0.000356 8.45E-05 4.2159
77
0.0001536
52
0.000185 0.00052
8 X Variable 16 -0.00021 0.001678 -
0.1274
3
0.8992879
18
-0.00361 0.00318
6

141

Figure 86: Measured DA versus Predicted DA: 45’ Depth Room and 8’ Height Light Shelf

Equation 8: DA Prediction for 45’ Depth Room with 8’ Height Light Shelf

( )

( )

x= Light Shelf Width
y=Light Shelf Curvature
z= Light Shelf Tilt Angle

0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
0 5 10 15 20
DA(simulation)
DA(predicted)

142

6.3.7. 50’Depth Room, 7’ Height Light Shelf

Table 22: Excel Regression Analysis Report: 50’ Depth Room and 7’ Height Light Shelf
SUMMARY OUTPUT

Regression Statistics

Multiple R 0.994455

R Square 0.988941

Adjusted R
Square
0.947302

Standard
Error
0.492916

Observations 44

ANOVA

df SS MS F Significanc
e F

Regression 16 608.356 38.022
25
166.92485
08
9.02E-23

Residual 28 6.803049 0.2429
66

Total 44 615.1591

Coefficients Standard
Error
t Stat P-value Lower 95% Upper
95% Intercept 1.42E-14 0.381811 3.72E-
14
1 -0.7821 0.78210
4 X Variable 1 1.57E-15 0.149759 1.05E-
14
1 -0.30677 0.30676
7 X Variable 2 -0.0188 0.002792 -
6.7327
2.61047E-
07
-0.02452 -
0.01308 X Variable 3 -0.0064 0.002913 -
2.1957
4
0.0365604
39
-0.01236 -
0.00043 X Variable 4 0.19187 0.086894 2.2081
03
0.0355956
08
0.013877 0.36986
3 X Variable 5 0.536542 0.082045 6.5395
75
4.33982E-
07
0.36848 0.70460
4 X Variable 6 2.81E-05 6.54E-06 4.3001
38
0.0001870
32
1.47E-05 4.15E-
05 X Variable 7 0 0 65535 #NUM! 0 0
X Variable 8 -0.00058 0.000138 -
4.2003
7
#NUM! -0.00086 -0.0003
X Variable 9 -0.00021 0.000148 -
1.4486
6
0.1585388
07
-0.00052 8.87E-
05 X Variable 10 0.18262 0.029206 6.2528
55
9.29342E-
07
0.122795 0.24244
6 X Variable 11 -0.00409 0.00097 -
4.2188
1
0.0002331
01
-0.00608 -
0.00211 X Variable 12 -0.05203 0.030102 -
1.7285
6
0.0949025
05
-0.11369 0.00962
8 X Variable 13 0.001734 0.001017 1.7055
67
0.0991601
18
-0.00035 0.00381
7 X Variable 14 -1.3E-05 1.71E-06 -
7.3811
2
4.88244E-
08
-1.6E-05 -9.1E-
06 X Variable 15 0.0005 7.3E-05 6.8535
62
1.90297E-
07
0.000351 0.00065
X Variable 16 -0.00551 0.001558 -
3.5391
4
0.0014237
05
-0.00871 -
0.00232

143

Figure 87: Measured DA versus Predicted DA: 50’ Depth Room and 7’ Height Light Shelf

Equation 9: DA Prediction for 50’ Depth Room with 7’ Height Light Shelf
( )

( )

( )

x= Light Shelf Width
y=Light Shelf Curvature
z= Light Shelf Tilt Angle

-2.0
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
0 2 4 6 8 10 12 14
DA (simulation)
DA(predicted)

144

6.3.8. 50’Depth Room, 8’ Height Light Shelf

Table 23: Excel Regression Analysis Report: 50’ Depth Room and 8’ Height Light Shelf
SUMMARY OUTPUT

Regression Statistics

Multiple R 0.990981

R Square 0.982044

Adjusted R
Square
0.911525

Standard
Error
0.562731

Observations 34

ANOVA

df SS MS F Significanc
e F

Regression 16 311.7412 19.483
82
65.629721
36
4.09E-12

Residual 18 5.7 0.3166
67

Total 34 317.4412

Coefficients Standard
Error
t Stat P-value Lower 95% Upper
95% Intercept -1.1E-15 0.613222 -1.7E-
15
1 -1.28833 1.28833
2 X Variable 1 -3.4E-16 0.24367 -1.4E-
15
1 -0.51193 0.51193
1 X Variable 2 -0.03222 0.003686 -
8.7421
7
6.77422E-
08
-0.03997 -
0.02448 X Variable 3 -0.00444 0.003686 -
1.2058
2
0.2434999
39
-0.01219 0.00329
9 X Variable 4 0.133333 0.112839 1.1816
25
0.2527312
16
-0.10373 0.37039
9 X Variable 5 0.883333 0.112839 7.8282
63
3.33358E-
07
0.646267 1.12039
9 X Variable 6 2.59E-05 8.28E-06 3.1295
9
0.0057917
38
8.52E-06 4.33E-
05 X Variable 7 0 0 65535 #NUM! 0 0
X Variable 8 -0.00093 0.000181 -
5.1234
9
#NUM! -0.00131 -
0.00055 X Variable 9 0.000259 0.000181 1.4345
78
0.1685541
22
-0.00012 0.00063
9 X Variable 10 0.04 0.042309 0.9454
27
0.3569603
85
-0.04889 0.12888
8 X Variable 11 0.001333 0.001363 0.9784
38
0.3408259
91
-0.00153 0.00419
6 X Variable 12 -0.04 0.042309 -
0.9454
3
0.3569603
85
-0.12889 0.04888
8 X Variable 13 0.001333 0.001363 0.9784
38
0.3408259
91
-0.00153 0.00419
6 X Variable 14 -3.7E-06 2.15E-06 -
1.7251
2
0.1016341
16
-8.2E-06 8.07E-
07 X Variable 15 1.4E-18 9.13E-05 1.54E-
14
1 -0.00019 0.00019
2 X Variable 16 0.000778 0.002005 0.3878
3
0.7026896
55
-0.00344 0.00499
1

145

Figure 88: Measured DA versus Predicted DA: 50’ Depth Room and 8’ Height Light Shelf

Equation 10: DA Prediction for 50’ Depth Room with 8’ Height Light Shelf
( )

( )

( )

( )

x= Light Shelf Width
y=Light Shelf Curvature
z= Light Shelf Tilt Angle
These formulae can be placed in an Excel sheet to simplify calculation, or in a small
separate program, which prompts the user for the appropriate input.
-2.0
0.0
2.0
4.0
6.0
8.0
10.0
12.0
0 2 4 6 8 10
DA (simulation)
DA(predicted)

146

Chapter 7 Conclusion and Future Work
This chapter provides a summary of the work in this thesis and presents the conclusion of
the discussion based on the discussion in previous chapters. The possible method for
future study is also included.

147

7.1 Condition of the Study
The main objective of this thesis is to create design assistant tools to help architects and
consultants in designing an efficient light shelf system. However, only the designs of the
buildings in this study in terms of window to wall ratio, orientation and ceiling height as
discussed in Chapters 3 are the basis for the conclusions and the recommended guidelines
of the light shelf design. Therefore, these conclusions and recommendations would vary
relative to the variation in building design attributes.
7.2 Tested Hypothesis
The dependent variables included in this study are the daylight penetration depth; the
independent variables are light shelf width, tilt angle, curvature and height, and room
depth. This study has reached the objectives that were represented in Chapter 1.
1. Demonstrate that the multiple variables that affect the performance of light
shelves are interacting with each other and need to be analyzed together.
2. Determine the appropriate indicators and criteria to evaluate light shelf daylight
performance.
3. Develop a workflow that architects and consultants can use to determine light
shelf daylight performance using popular design software.
4. Compare building daylighting penetration of a case of south-facing fenestration
with the optimum light shelf combination to a base case without a light shelf.

148

5. Determine the optimum light shelf based on multiple variables of three typical
office rooms which facing south.
6. Develop a design assistant guideline or tool that can help architects or consultants
design light shelves.
7.3 Conclusion
A light shelf is a kind of daylight redirecting device that redirects light from the window
to the back of the room and sometimes increases daylight penetration depth. Because
there are many variables that could affect light shelf performance, it is difficult for
architects and consultants to design an efficient light shelf. Creating light shelf design
assistant tools that help architects and consultants to figure out the appropriate light shelf
configurations when they design a light shelf is the final goal of this study.
A study of the simulation of lightshelves configuration and its impact on daylighting
penetration depth inside office spaces was conducted using DIVA for Grasshopper. The
main contribution of this study was evaluating the effect of different light shelf variables
together instead of evaluating them separately. The evaluation of lightshelves
performance is dependent on running hundreds of configurations using a genetic
algorithm tool - in this study, Galapagos. The study was split into two sections: an
introduction of how different light shelf variables can affect light shelf performance and
an algorithm-based design tool for architects and consultants to find the optimum light
shelf in a certain space. In the first section, variables that affect light shelf performance
(light shelf curvature, tilt angle, width and height) in three certain depth rooms are

149

evaluated and discussed to find their effect on light shelf performance. In the second
section, three products are created: guideline of diagrams for designers to quickly define
the appropriate light shelf configuration for a certain room, equations for users to quickly
get the DA value prediction at rear of the room, and a workflow that architects and
consultants can use to get a precise simulation results of light shelf daylight performance
by themselves based on DIVA for Grasshopper.
DIVA was used as the simulation tool for this study, using “Radiance” as its calculation
engine. Daylight Autonomy is used as performance criteria to measure daylight
penetration depth of the room.
The results shows that light shelves can improve the penetration depth of daylighting in
rooms, but it is not a universal good choice for all rooms. Some small-depth rooms are
already bright enough that they do not need a light shelf, while some deep rooms may be
so deep that the light shelf cannot help all the way to the back. However, light shelf could
still help deep room to improve their daylight penetration depth even though DA increase
is not obvious at very back of the room. 25 feet depth and 30’ depth room without any
light shelf already has 95% and 89% Daylight Autonomy at rear of the room. For rooms
less than 30’ deep, a light shelf will not greatly improve daylight penetration depth
because they already have enough daylight. Also, a light shelf will not have great impact
on increasing the Daylight Autonomy value at the rear of the room for the room deeper
than 50 feet. For instance, in a 55’ deep room, the light shelf could only increase Daylight
Autonomy at rear of the room from 0% to 2%, which is not close to sufficient daylight
requirement. For this reason, only rooms of 35’, 40’, 45’ and 50’ depth are selected as
test cases for further simulation and analysis in this study.

150

After running hundreds of simulations, results show that a light shelf has a greater
potential to enhance the indoor luminous environment when designed appropriately. For
a 35’ depth room, the best case of light shelf in this study could increase the Daylight
Autonomy (DA) at rear of the room from 45 to 75. For a 40’ depth room, the best case of
light shelf could increase DA from 25 to 52. For 45’ and 50’ depth rooms, the DA
increase would be 7 to 23 and 0 to 10.
However, none of the flat horizontal light shelf cases function well in this study,
regardless of orientation, room depth, window size and the material they are made of.
The only possibility that could increase flat horizontal light shelf performance lies in
change of the ceiling geometry; this could also be a future direction for study.
Studies of former researchers only consider light shelf parameter individually, but from
the analysis in Chapter 5, we can get the idea that each variables of light shelf should be
considered together instead of separately. For example, a 7’ height, 2’ depth, and 15
degree curvature, 30 degree tilt angle light shelf has the same DA value with the 8’ height,
4’ depth, and 15 degree curvature, 30 degree tilt angle light shelf. When designing a light
shelf, all the variables should be thought about in a more integrated way.
For rooms from 35’ to 50’ depth, the increase of the light shelf width has a positive
impact on room daylight penetration depth. However, light shelf width is not a key factor
in improvig light shelf performance.
The impact of light shelf curvature on the tested DA value of the room is relatively
complex. For 35’ depth and 40’ depth room, there is not a clear relationship between light

151

shelf curvature and DA. For 45’ depth room and 50’ depth room, curvature of 15 degree
has the most positive affect on DA improvement in range of 0 to 30 degree.
Among all four variables, tilt angle has the most significant impact on DA at the rear of
the room. For 35’, 40’ and 45’ deep room, the bigger the light shelf angle the bigger the
DA. But when room is 50’ deep, the relationship between light shelf angle and DA is not
that simple. 15 degree tilt angle has the most positive impact on the increase of DA.
In this study, light shelf height only has two values, 7 feet and 8 feet. For 35’, 40’ and 45’
depth rooms, a 7’ height light shelf has a better performance than an 8’ light shelf. For a
50’ depth room, there is no clear advantage for each height light shelf.
Future work could include a more meaningful overview and research about glare and
daylight uniformity of the room. Daylight Autonomy is not an appropriate performance
criterion to measure daylight uniformity of the space. Illuminance levels of different
times of a year should be used to measure daylight uniformity in the future study.

7.4 Future Study
Three major developments could be the likely next steps in this study: adding more
variables, employing more performance criteria other than daylight penetration depth and
creating design assistant plugins for Rhino and Grasshopper.

152

7.4.1 More Variables
This study gives an example of using parametric methods and software such as
Grasshopper and Galapagos to quickly complete a considerable number of simulations,
and future studies could reference this case and complete more explorations of variables.
For example, while this study only focuses on external light shelf evaluation, future
studies could take internal light shelf and combination of both internal and external light
shelf into consideration to explore more possible improvements. Also, some complex
light redirection systems such as an anidolic system could also be taken into
consideration, because such systems still have certain variables that could be easily
modeled and controlled by parametric software. Also, an anidolic system has been
demonstrated by others to be highly efficient as described in Chapter 2.
Another variable that could be explored is the ceiling configuration. The impact of ceiling
configuration is already been introduced in Chapter 2, and it could maximize light shelf
function if being used properly. For a flat horizontal light shelf, optimum ceiling
configuration may be able to improve its performance although it currently shows no
effect on daylight penetration depth increase. Changing ceiling configuration from flat to
sloped or curved could have unexpected impact on room daylight performance.
Parametric method is a good way to optimize the ceiling configuration by control its
variables.
Moreover, window size should be considered in the future study. Although a lot of
buildings right now use wall to wall windows, some building still use small size window.

153

Light shelves could be a daylight retrofit strategy to be employed in some existing
buildings and in such case; the window size has to be considered.
7.4.2 More Performance Criteria
Light shelves redirect the light into the rear of the room. The most important function of a
light shelf is to increase the daylight penetration depth. Daylight Autonomy is used as the
main performance criterion; this criterion could measure the daylight penetration depth
on a year base and take climate and orientation into consideration. A Light shelf is also
able to function as shading and shade the front of the room and thus increase the daylight
uniformity and decrease the contrast of light of the room. Therefore, daylight uniformity
is also an important aspect when judging the light shelf performance. However, it is hard
to use Daylight Autonomy to measure daylight uniformity of the space. Illuminance level
of different time during a year under different sky conditions is a more suitable
performance criterion for daylight uniformity studies.
Another criteria should be taken into consideration is glare. Glare is visual discomfort
caused by an uncomfortably bright light source or reflection, and glare is an underutilized
parameter in contemporary architectural design. In its simplest form, glare is a
consequence of the inability of the human eye to adapt to different light levels. Glare is a
complex problem and deserves careful consideration; future work should take this
criterion into light shelf evaluation and get a full understanding of the room daylight
performance.
Energy is also an important criterion when judging a light shelf performance. A light
shelf could increase daylight penetration depth and thus save electric energy by reducing

154

the time of using electric lighting. A future study could involve energy saving simulation
using Designbuilder or DIVA. DIVA allows the modeling of single-zone thermal models
using EnergyPlus as simulation engine. It allows users to test the relative effects of
different daylighting and controls strategies on the energy consumption of a typical daylit
space.
7.4.3 A Design Assistant Plugin for Rhino and Grasshopper
It is valuable to further develop a design assistant plugin based on popular design model
software such as Rhino and Grasshopper to help architects and consultants to design light
shelves. This research stopped with guideline diagrams and quick calculation equations.
But a plugin would be more convenient for users to compare different light shelf
strategies and find the optimum light shelf. A more successful product could
automatically recognize the building information, which include room size and window
to wall ratio etc., and could automatically create the optimized light shelf model
according to the limit and preference given by the users. Users could quickly get a visual
presentation of the light shelves and also a feedback of how is the performance of such
light shelves. Such plugin could be based on the data collected from this study.

155

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Abstract (if available)

Abstract The transmission of sufficient daylight to offset electrical lighting, while maintaining comfortable conditions for occupants, is the central objective for effective daylighting. Utilizing a light shelf is a common strategy for enabling daylight transmission while controlling direct sun and discomfort glare to maintain occupant comfort. ❧ However, it is difficult for designers to optimize light shelf performance during design, as they are required to choose from many different possible design configurations, each with multiple variables (e.g. geometry, surface properties, and position within the facade). This study presents a method for optimizing light shelf daylighting and visual comfort performance that utilizes Diva for Rhino combined with parametric analysis and optimization to develop an integrated solution based on multiple variables input by the user. The method is discussed in the context of results from room simulations and façade optimization of a large commercial office building located in downtown Los Angeles. The study concludes with recommendations for implementing this method in the context of early-stage design decision-making to support energy reduction and improved occupant comfort in commercial office buildings incorporating light shelves.

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Asset Metadata

Creator Liu, Yue (author)

Core Title Effective light shelf and form finding: development of a light shelf design assistant tool using parametric methods

School School of Architecture

Degree Master of Building Science

Degree Program Building Science

Publication Date 07/23/2013

Defense Date 07/23/2013

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

Tag daylight autonomy,design assistant tool,DIVA,light shelf,OAI-PMH Harvest,Office Building,Radiance

Format application/pdf (imt)

Language English

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Advisor Noble, Douglas (committee chair), Konis, Kyle (committee member), Schiler, Marc (committee member)

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Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-298314

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