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Pushing the solar envelope: determining solar envelope generating principles for sites with existing buildings

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Content i

PUSHING THE SOLAR ENVELOPE

Determining solar envelope generating principles for sites with existing buildings

By

Shinjini Bhattacharjee

Thesis

Presented to the
FACULTY OF THE
SCHOOL OF ARCHITECTURE
UNIVERSITY OF SOUTHERN CALIFORNIA
In partial fulfilment of the
Requirements of degree
MASTER OF BUILDING SCIENCE

MAY 2016

ii

COMMITTEE

Douglas Noble, FAIA, Ph.D.
Associate Professor
USC School of Architecture
dnoble@usc.edu
(213) 740-2723

Karen M. Kensek, LEED AP BD+C, Assoc. AIA
Assistant Professor
USC School of Architecture
kensek@usc.edu
(213)740-2081

Marc Schiler, FASES, LC
Professor
USC School of Architecture
marcs@usc.edu
(213)740-4591

iii

ACKNOWLEDGEMENTS

This thesis, like any other human endeavour, is a result of not just my own efforts. There are a number of people without
whom this thesis may not have been completed and to whom to whom I’m greatly indebted.
To my father for his never-ending enthusiasm for my thesis work, and to my mother for all her insights and tips for this
thesis, and for staying up late into night to read my work, a special thank you to you both. And also for the myriad ways in
which, throughout my life, you have actively supported me in all my endeavours.
My gratitude to my thesis committee Douglas Noble, Karen Kensek, and Marc Schiler for all their inputs and discussions.
Their encouragement and support were essential in accomplishing this work.
Special thanks to Professor Ralph Knowles, for it was on his suggestion that this research was carried out.
To all my MBS friends Sunny, Kim, Lisha, Kelly, Joyce, Maral, Brittany, Aditya, Kai, Dennis, Edna, Mohammed, Jay, and
Ilaria for all their kind words of encouragement.
And lastly, to my friends Shreya and Gayatri, for supporting me through all the deadlines, and celebrating all my successes.
iv

ABSTRACT
A solar envelope for a site is the largest volume that can be built that allows solar access to neighbouring buildings for a
specified period of time in a day (Knowles 1981). Solar envelope principles are important for low-energy, passive
architecture on the neighbourhood scale.
The concept and generation of a solar envelope is based on the daily and annual movement of the sun across the sky, which
defines the maximum buildable volume for a building while still allowing solar access for neighbouring buildings. When
applied as a zoning tool over a neighbourhood, solar envelopes ensure solar access for all buildings. With guaranteed access
to sunlight, designers can choose to use that resource for daylighting, energy generation, and passive heating (Knowles
1980).
Buildings that have already been built without considering solar envelope constraints might cast undesirable shadows on
neighbouring sites. Any additions made to such a site and the building geometry may result in additional shadow being cast
on to the surroundings. Using similar principles to those used to generate solar envelopes, how much more can be added to
the existing building geometry without casting additional shadows beyond the site has been determined. For this purpose, a
solar envelope generation tool has been created in Dynamo, to work with Revit, based on user input. User inputs are site
location (latitude and longitude), envelope cut-off times, site grid orientation, and shadow fence.
Five building geometries were tested – a rectangular geometry, and four L-shaped geometries in different orientations. The
site location (latitude and longitude) and envelope cut-off times were varied in each case, solar envelopes for the sides of the
building were generated, and the change in building volume was calculated.
The principles were then applied to 6 blocks in a commercial district of Los Angeles, and the increase in floor area ratios
(without further impacting solar access of the surrounding buildings) was calculated.
The test cases were modelled in Revit as conceptual masses. Solar envelopes, whenever required, were generated using the
tool and imported into Revit. Additional volumes were also modelled in place on the test cases as conceptual masses.
Results show that typically additional volume is possible that does not cast additional shadows within the specific time of the
day. The amount of volume added changes with the location of the site and the desired cut-off times.
This information could be part of zoning ordinances, controlling additions and renovations to existing buildings not built
within a solar envelope, to prevent additional shadows being cast as a result of additions. Conversely, these principles could
be used by existing buildings to make renovations and additions to the building geometry, without further impacting the solar
access of the surrounding buildings.
HYPOTHESIS
Solar envelope principles can be used to determine envelope geometry for sites with existing buildings. The envelope volume
generated can be useful in making additions to buildings.

v

TABLE OF CONTENTS

COMMITTEE............................................................................................................................................................................ ii
ACKNOWLEDGEMENTS .................................................................................................................................................... iii
ABSTRACT .............................................................................................................................................................................. iv
HYPOTHESIS .......................................................................................................................................................................... iv
TABLE OF CONTENTS .......................................................................................................................................................... v
LIST OF FIGURES ............................................................................................................................................................... viii
LIST OF TABLES ..................................................................................................................................................................... x
CHAPTER 1
1. INTRODUCTION ............................................................................................................................................................ 11
1.1. Hypothesis statement corollary ................................................................................................................................ 11
1.2. Solar design strategies .............................................................................................................................................. 11
1.2.1. Passive solar design ......................................................................................................................................... 11
1.2.2. Active solar design .......................................................................................................................................... 11
1.2.3. Effect on HVAC equipment ............................................................................................................................ 11
1.2.4. Daylighting ...................................................................................................................................................... 12
1.2.5. Solar energy flow in buildings ......................................................................................................................... 12
1.3. The Sun’s movement ................................................................................................................................................ 12
1.3.1. Sun’s daily movement ..................................................................................................................................... 12
1.3.2. Sun’s annual movement ................................................................................................................................... 13
1.3.3. Sun position terminology ................................................................................................................................. 13
1.4. Solar access .............................................................................................................................................................. 16
1.4.1. Precedents ........................................................................................................................................................ 17
1.4.2. Solar access zoning .......................................................................................................................................... 18
1.4.3. California Solar Rights Act ............................................................................................................................. 19
1.5. Scope of work .......................................................................................................................................................... 19
1.6. Application of work ................................................................................................................................................. 20
CHAPTER 2
2. BACKGROUND .............................................................................................................................................................. 21
2.1. The solar envelope ................................................................................................................................................... 21
2.2. Solar envelope principles ......................................................................................................................................... 21
2.3. Generating solar envelopes ..................................................................................................................................... 21
2.4. Factors affecting solar envelope geometry ............................................................................................................... 23
2.4.1. Site dimensions ................................................................................................................................................ 23
2.4.2. Site orientation................................................................................................................................................. 24
2.4.3. Site slope ......................................................................................................................................................... 25
2.4.4. Latitude ............................................................................................................................................................ 26
2.4.5. Cut-off times .................................................................................................................................................... 26
2.5. Shadow fence ........................................................................................................................................................... 27
2.6. Computer aided solar envelope generation techniques ............................................................................................ 27
vi

2.6.1. Grid and Flag Pole ........................................................................................................................................... 27
2.6.2. Cutting Solids .................................................................................................................................................. 27
2.6.3. Boolean Intersection ........................................................................................................................................ 27
2.7. Previous solar envelope generating tools ................................................................................................................. 28
2.7.1. SolCAD ........................................................................................................................................................... 28
2.7.2. SolVelope ........................................................................................................................................................ 28
2.7.3. CalcSolar ......................................................................................................................................................... 28
2.7.4. DIVA for Rhino ............................................................................................................................................... 29
2.7.5. Right to Light in Ecotect ................................................................................................................................. 29
2.7.6. Solar envelope generator for BIM using Revit API ......................................................................................... 29
2.8. Chapter summary ..................................................................................................................................................... 29
CHAPTER 3
3. METHODS ....................................................................................................................................................................... 30
3.1. Solar envelope tool generation ................................................................................................................................. 30
3.1.1. Dynamo script ...................................................................................................................................................... 30
3.1.2. Test cases ............................................................................................................................................................. 30
3.2. Solar envelopes for sites with existing buildings ..................................................................................................... 31
3.2.1. Establish test cases .......................................................................................................................................... 31
3.2.2. Envelope generation ........................................................................................................................................ 32
3.3. Urban Application .................................................................................................................................................... 34
3.4. Script algorithm ........................................................................................................................................................ 36
3.4.1. Step 1 ............................................................................................................................................................... 37
3.4.2. Step 2 ............................................................................................................................................................... 37
3.4.3. Step 3 ............................................................................................................................................................... 41
3.4.4. Step 4 ............................................................................................................................................................... 49
3.5. Chapter summary ..................................................................................................................................................... 51
CHAPTER 4
4. RESULTS ......................................................................................................................................................................... 52
4.1. Test for volume vs. latitude and cut-off times .......................................................................................................... 52
4.2. Urban application results .......................................................................................................................................... 54
4.2.1. Example calculation of increase in usable floor area ....................................................................................... 55
4.3. Chapter summary ..................................................................................................................................................... 60
CHAPTER 5
5. ANALYSIS ....................................................................................................................................................................... 61
5.1. Site location vs. volume added ................................................................................................................................. 61
5.2. Cut-off times vs. volume added ............................................................................................................................... 63
5.3. Urban application ..................................................................................................................................................... 65
5.4. Chapter summary ..................................................................................................................................................... 67
CHAPTER 6
6. CONCLUSIONS ............................................................................................................................................................... 68
6.1. Applications ............................................................................................................................................................. 68
vii

6.2. Urban application constraints ................................................................................................................................... 69
6.3. Summary .................................................................................................................................................................. 69
CHAPTER 7
7. FUTURE WORK .............................................................................................................................................................. 71
7.1. Add other features to the Dynamo tool for generating solar envelopes. .................................................................. 71
7.2. Test principles for other geometries. ........................................................................................................................ 71
7.3. Test other factors that affect solar envelope geometry ............................................................................................. 71
7.4. Further urban applications study .............................................................................................................................. 72
7.5. Chapter summary ..................................................................................................................................................... 72
APPENDIX ............................................................................................................................................................................... 73
A. The Dynamo script ....................................................................................................................................................... 73
B. Inputs ............................................................................................................................................................................ 73
C. Site boundaries ............................................................................................................................................................. 74
D. Summer solar angles ..................................................................................................................................................... 74
E. Winter solar angles ....................................................................................................................................................... 75
F. Summer ridge points ..................................................................................................................................................... 76
G. Winter ridge points ....................................................................................................................................................... 76
H. Determination of envelope height ................................................................................................................................. 77
I. Geometry generation .................................................................................................................................................... 77
J. Outputs ......................................................................................................................................................................... 78
K. .sat output ..................................................................................................................................................................... 78
L. Import directly to Revit ................................................................................................................................................ 78
M. Side envelope generation.......................................................................................................................................... 79
BIBLIOGRAPHY .................................................................................................................................................................... 80
viii

LIST OF FIGURES

Figure 1- Sun’s daily movement. Source - www.wordpress.mrreid.org .................................................................................... 13
Figure 2 - Sun’s annual movement. Source - www.nuffieldfoundation.org .............................................................................. 13
Figure 3 - Altitude and azimuth of the sun. Source - www.wiki.naturalfrequency.com ............................................................ 14
Figure 4 - Hour Angle. Source - www.appropedia.org .............................................................................................................. 15
Figure 5 - Solar declination angle (δ) throughout the year. As the earth orbits around the sun, the angle between the
earth’s equatorial plane and orbital plane varies from -23.45° to 23.45°. Source - www.blc.lsbu.ac.uk ................................... 16
Figure 6 - The Greek planners of Olynthus arranged houses to have two fronts: one to the sun and one to the street. The
diagram shows the approximate location of south-facing courtyards centering each house. (North, up.). [Image and
caption courtesy – Ralph Knowles] ........................................................................................................................................... 17
Figure 7 - Acoma Pueblo. Thick masonry walls and timber roof-terraces respond well to seasonal migrations of the
sun (left). The spacing between Acoma's rows of houses is strategic: just far enough to avoid winter shadows while
conserving precious space on a high, small plateau (right). [Image and caption courtesy – Ralph Knowles] ........................... 17
Figure 8 - The winter sun angles reach deep into the cliff dwellings at Mesa Verde, while the summer rays are blocked
by the overhanging cliff. [Image and caption courtesy – Ralph Knowles] ................................................................................ 18
Figure 9 - – Boundary determination for east and west sides. Source – Sun Rhythm Form - Chapter 3: Solar Envelope
of Sun Rhythm Form (Knowles, 1981 pp.54 -6) ....................................................................................................................... 22
Figure 10 - Boundary determination for north and south sides. Source – Sun Rhythm Form - Chapter 3: Solar Envelope
of Sun Rhythm Form (Knowles, 1981 pp.54 -6) ....................................................................................................................... 22
Figure 11 – The complete envelope. Source – Sun Rhythm Form - Chapter 3: Solar Envelope of Sun Rhythm Form
(Knowles, 1981 pp.54 -6) .......................................................................................................................................................... 22
Figure 12 – Complex solar envelopes. Source – Sun Rhythm Form - Chapter 3: Solar Envelope of Sun Rhythm Form
(Knowles, 1981 pp.54 -6) .......................................................................................................................................................... 23
Figure 13 - Solar envelope varying with site dimensions. Source - Sun Rhythm Form - Chapter 3: Solar Envelope of
Sun Rhythm Form (Knowles, 1981 pp.65) ................................................................................................................................ 23
Figure 14 - Shadow patterns for different street orientation. Source - Ralph Knowles - Sun, Rhythm Form,
MIT Press 1981.......................................................................................................................................................................... 24
Figure 15 - Three different block orientations demonstrate the effect on size and shape of solar envelopes. Image -
Ralph Knowles, Sun Rhythm Form, MIT Press, 1981 .............................................................................................................. 25
Figure 16 - – Solar envelope varying with grid orientation. Source - Sun Rhythm Form - Chapter 3: Solar Envelope of
Sun Rhythm Form (Knowles, 1981 pp.65 -71) .......................................................................................................................... 25
Figure 17 - – Solar envelope varying with slope. Source - Sun Rhythm Form - Chapter 3: Solar Envelope of
Sun Rhythm Form (Knowles, 1981 pp.65 -71) .......................................................................................................................... 26
Figure 18 – Solar envelope varying with latitude. Source - Sun Rhythm Form - Chapter 3: Solar Envelope of
Sun Rhythm Form (Knowles, 1981 pp.65 -71) .......................................................................................................................... 26
Figure 19 - Solar envelope varying with cut-off times. Source - Sun Rhythm Form - Chapter 3: Solar Envelope of Sun
Rhythm Form (Knowles, 1981 pp.65 -71) ................................................................................................................................. 26
Figure 20 - Solar envelope varying with shadow fence. Source - Sun Rhythm Form - Chapter 3: Solar Envelope of Sun
Rhythm Form (Knowles, 1981 pp. 105) .................................................................................................................................... 27
Figure 21 - Envelope generation in SolCAD. [Image courtesy – Manu Juyal.] ........................................................................ 28
Figure 22 - Solar envelope generated using the tool - a. Within the cut-off times. b. Outside the cut-off times ....................... 30
Figure 23 - Solar envelope generated using the tool, with different site dimension and different location -
a. Within the cut-off times. b. Outside the cut-off times ............................................................................................................ 31
Figure 24 - Solar envelope generated using the tool, with different grid orientation - a. Within the cut-off times.
b. Outside the cut-off times ........................................................................................................................................................ 31
Figure 25 - The five building geometries tested. ....................................................................................................................... 32
Figure 26 - The first place to add additional volume. Anything built within the solar envelope for the empty site
will not cast additional shadows. If the building occupies the whole site, this addition is not possible. ................................... 32
Figure 27 - The second place to add volume - on the roof. The roof can be considered as a site itself, and a
corresponding envelope be generated for the same. .................................................................................................................. 33
Figure 28 – Conditions for adding volume to building sides. .................................................................................................... 33
Figure 29 - Steps to generate solar envelope for the sides of the building. ................................................................................ 34
Figure 30 - The complete envelope generation. ......................................................................................................................... 34
Figure 31 - The area under study in Downtown Los Angeles. .................................................................................................. 35
Figure 32 – A visual overview of the complete script. .............................................................................................................. 36
Figure 33 - Script algorithm ....................................................................................................................................................... 36
ix

Figure 34 - The user inputs ........................................................................................................................................................ 37
Figure 35 - The site information. ............................................................................................................................................... 37
Figure 36 - Calculating co-ordinates for site edge point A ........................................................................................................ 38
Figure 37 - Calculating co-ordinates for site edge point B ........................................................................................................ 39
Figure 38- Calculating co-ordinates for site edge point C ......................................................................................................... 40
Figure 39 - Accounting for shadow fence .................................................................................................................................. 41
Figure 40 - Part of the Dynamo script for finding site edge points ............................................................................................ 41
Figure 41 - Part of the Dynamo script for finding solar altitude for summer ............................................................................ 43
Figure 42 - Part of the Dynamo script for finding solar altitude for winter ............................................................................... 44
Figure 43 - Part of the Dynamo script for finding solar azimuth for summer ........................................................................... 44
Figure 44 - Part of the Dynamo script for finding solar azimuth for winter .............................................................................. 45
Figure 45 - Calculating coordinates for summer ridge point ..................................................................................................... 45
Figure 46 - Part of the Dynamo script for finding x Coordinate for summer ridge point .......................................................... 46
Figure 47 - Part of the Dynamo script for finding y Coordinate for summer ridge point .......................................................... 46
Figure 48 - Part of the Dynamo script for finding z Coordinate for summer ridge point .......................................................... 47
Figure 49 - Part of the Dynamo script for finding x Coordinate for winter ridge point ............................................................. 47
Figure 50 - Part of the Dynamo script for finding y Coordinate for winter ridge point ............................................................. 48
Figure 51 - Part of the Dynamo script for finding z Coordinate for winter ridge point ............................................................. 48
Figure 52 - Comparing Z-coordinate values .............................................................................................................................. 48
Figure 53 - Envelope shape when grid orientation is zero v. when it is not zero. S and W are the summer and
winter ridge points. Changing the grid orientation moves these points and changes the order of joining them. ....................... 49
Figure 54 - Part of the Dynamo script where the code determines which of the four possible outputs to follow...................... 49
Figure 55 – Joining of the vertices when grid orientation is a) zero, b) not zero. ...................................................................... 49
Figure 56 - Joining points for shadow fence .............................................................................................................................. 50
Figure 57 - The five possible outputs ........................................................................................................................................ 50
Figure 58 – The .sat output box. Users have a choice of output units ....................................................................................... 50
Figure 59 - Import to Revit ........................................................................................................................................................ 50
Figure 60 - Test case examples .................................................................................................................................................. 52
Figure 61 - Key plan for buildings. ............................................................................................................................................ 55
Figure 62 - Addition and calculation of new floors and floor areas. ......................................................................................... 56
Figure 63 - Latitude versus site and roof envelope heights for the same rectangular building. ................................................. 61
Figure 64 - Latitude and cut-off times v. Envelope volume - Rectangular geometry. ............................................................... 62
Figure 65 - Latitude v. Envelope volume added - L-geometry, 4 orientations. The cut-off time has been kept the same
in all 4 cases (summer 7am-5pm, winter 9am-3pm) .................................................................................................................. 63
Figure 66 - Effect of cut-off times on the addition of building side envelope for different latitudes below and
above 23.5°N for the same cut-off times. For the same building, a side envelope can always be added if located below
23.5°N, but for locations above 23.5°N the addition of a side envelope is dependent on the cut-off times chosen. ................. 64
Figure 67 - Effect of cut-off times on the building side envelope added for sites located 23.5°N and up. For the
same location varying the cut-off times can result in volume being added to the building side or not. .................................... 65
Figure 68 - Comparison between original and new usable floor area values ............................................................................. 66
Figure 69 - Urban application results. The existing building geometries are in purple. The new envelopes added are in
white. ......................................................................................................................................................................................... 67
Figure 70 - Possibilities. This is an illustration showing what the solar envelope volume generated can be used for.
On the left is the original building. On the right are the possible uses. This shows the ideal scenario where the site and
the building can have all the three envelope volumes added. .................................................................................................... 69
Figure 71 - Examples of other building geometries that can be studied, in addition to the rectangular and L-shaped
geometries studied. .................................................................................................................................................................... 71
Figure 72 - Full Dynamo script with all add-ons ....................................................................................................................... 73
x

LIST OF TABLES
Table 1 - Percentage of volume added for rectangular geometry. ........................................................................... 53
Table 2 - Percentage of volume added for L-shaped geometries. ........................................................................... 53
Table 3 - Increase in usable floor area ..................................................................................................................... 57
11

CHAPTER 1
1. INTRODUCTION
“The sun is fundamental to all life. It is the source of our vision, our warmth, our energy, and the rhythm of our lives. Its
movements inform our perceptions of time and space and our scale in the universe. Assured access to the sun is this
important to the quality of our lives.” -- Ralph Knowles
1

With this is mind, a concept of solar envelopes was conceived and tested by Ralph Knowles, at the USC School of
Architecture. A solar envelope for a site is the virtual three-dimensional boundary, building within which enables solar access
for neighbouring buildings, for a certain period of time in the day. These imaginary boundaries are defined by the sun’s
relative motion throughout the day and also by the seasonal variation of the sun’s path.
1.1. Hypothesis statement corollary
For a site with an existing building, it is possible to generate solar envelopes for the whole sides of a building in order to
change the shape of the entire volume without casting additional shadows onto the neighbouring buildings. These additional
solar envelopes can be generated using similar techniques as those used for empty sites.
1.2. Solar design strategies
The sun and solar radiation have important roles on occupant comfort and energy consumption of a building. Although the
amount may vary, solar radiation and sunlight are available regardless of the location of the building site, and thus, cannot be
ignored. It is essential to consider solar design strategies in the early stages of any design. The sun provides light and heat,
both of which can be successfully regulated and incorporated into a building’s design to minimize dependence on fossil fuels
to provide lighting and thermal comfort. In most climates, solar heat gain is generally welcome in the winter, when it can
reduce heating costs, but it is rarely welcome in the summer, when it adds to cooling loads.
1.2.1. Passive solar design
Passive solar design strategies utilize solar heat gain and the principles of heat transfer and thermodynamics to heat a space or
keep it cool. These strategies take advantages of material properties and temperature differences caused by exposure to sun.
Passive strategies create systems that are simple, have little or no moving parts, and require no mechanical systems.
2

Strategies such as operable windows and shading devices, thermal mass, solar chimneys and solar collectors utilize solar heat
passively to provide thermal comfort in a space. The building form, in itself also plays an important role in passive solar
design.
3
In order to effectively use passive strategies in a building, it is important to know the period of assured solar access
in a day, making solar envelopes a key part of passive solar design.
1.2.2. Active solar design
In addition to the passive effects of solar heat gain, active solar technologies are used to generate electricity such as
photovoltaic panels or to transfer energy as heat such as domestic hot water heating systems or space heating systems. The
efficiencies of these systems depend on the amount of insolation (incident solar radiation) that they receive throughout the
year. Insolation levels determine the amount of electricity generated by the PV panels or the efficiency of hot water systems.
This is turn determines the economic payback period of these systems. This is where knowledge about assured solar access
becomes important. With assured solar access, system efficiencies and payback period can be easily calculated, proving when
such systems are more viable.
4

1.2.3. Effect on HVAC equipment
Effectively adding solar design strategies to a design can also help reduce HVAC equipment size and the need for electrical
lighting during the day. Designing so as to maximize solar heat gain during winter months or when the ambient temperature
is lower than the comfort level, and minimizing solar heat gain during summer, can reduce equipment sizes. This in turn, will
consume less fuel.

1
Ralph L Knowles, The solar envelope. Solar Law Reporter. 1980; 2(2):263.
2
"Passive Solar Design." Passive Solar Design. Accessed October 4, 2015. http://passivesolar.sustainablesources.com/
3
Ibid.
4
Alicyn E. Henkhaus, “Computer-Generated Solar Envelopes and Building Information Modeling (BIM)” (master’s thesis,
University of Southern California, 2012), 12.
12

1.2.4. Daylighting
In addition to controlling the thermal environment with solar design strategies, a building can be designed to maximize
daylight into the interior spaces, and reduce dependence on electric lighting. Daylighting is the controlled admission of
natural light into a building, for the purpose of lighting up the interior spaces. According to U.S. Green Building Council,
proper daylighting significantly reduces the need for artificial lighting, which reduces the energy demand by about 30-80%.
Additionally, studies have shown that daylighting can have large physiological and psychological benefits for humans.
Daylighting improves sleep patterns, increases worker productivity, shortens patient recovery times in hospitals, and
improves or increases student test scores, retail purchase behaviour, alertness, mood, atmosphere, memory, and health.
Admitting daylighting into a space, thus, comes with a large number of benefits.
5

Designing for daylighting needs to consider both how to provide enough daylight to a space and designing to avoid
undesirable side effects resulting from insufficient daylight
6
One of the common side effects is glare. Direct sunlight causes
uncomfortable glare. Diffused daylight is more desirable. If a window lets in direct sunlight, not only does this cause glare,
but also lets in solar heat. Care must be taken, while designing for daylighting that only diffused daylight is let in to the space
and not direct sunlight. Trying to diffuse direct sunlight is different and rarely effective, without careful shielding.
1.2.5. Solar energy flow in buildings
Energy from the sun is received in primarily two forms – as heat and light. Facades play an important role in the flow of
energy through a building, especially heat energy. Heat flows through facades by three means – conduction, convection and
radiation. Conduction is the transfer of heat between two objects which are in contact with each other. Convection is the
transfer of heat caused by the movement of fluids, where they heat up and rise, taking the heat energy with them. Radiant
transfer of heat occurs via electromagnetic waves.
7

In a building, conduction occurs through all envelope components, such as the wall and the roof. Convective heat transfer
takes place as a result of wind or pressure driven air movement. Radiant heat transfer occurs through windows and other
glazed parts of the facades.
8

If a building has an assured access to sun, during certain times of the day throughout the year, making such solar design
related decisions becomes easier on the part of the design team. Knowing the amount of heat and light through facades and
windows, and being able to control them as per requirement early on in the design stage will help designers to come up with
energy efficient designs for the building as a whole. This is why assured solar access becomes important.
1.3. The Sun’s movement
The sun has a daily and an annual movement path across the sky hemisphere. Daily, it rises along the eastern horizon and sets
on the western horizon. Throughout the year, its arc shifts along the north-south direction. Understanding how the sun moves
in a day, and over a year is the key to the generation of solar envelope geometry. The solar envelope is derived from the sun’s
position at different times of the day, and on different days of the year.
1.3.1. Sun’s daily movement
The sun’s daily movement follows a path from the eastern horizon to the western horizon, across the sky hemisphere. The
sun rises in the east, moves towards the southern horizon (or northern, if in the southern hemisphere), as it steadily climbs
across the sky, reaches its zenith at noon, and steadily climbs down, moving west and sets in the west. The exact location
where the sun rises and sets varies with the seasons as well as the latitude. During the summer season, the location of the
sunrise is towards the north of east, and the sun sets towards the north of west. On the equinoxes, the sun rises and sets
exactly due east and west respectively. During the winter months, the sun rises south of east and sets south of west (Figure 1).

5
"Daylighting Strategies" U.S. Green Building Council. Accessed August 15, 2015.
http://www.usgbc.org/education/sessions/daylighting-strategies-4775236
6
"Daylighting." Daylighting. Accessed August 2, 2015. http://www.wbdg.org/resources/daylighting.php
7
"Heat Energy Flows in Buildings | Sustainability Workshop." Heat Energy Flows in Buildings | Sustainability Workshop.
Accessed August 1, 2015. http://sustainabilityworkshop.autodesk.com/buildings/heat-energy-flows-buildings
8
Ibid.
13

Figure 1- Sun’s daily movement. Source - www.wordpress.mrreid.org
1.3.2. Sun’s annual movement
The sun’s path has a seasonal variation as well. During the summer months, the sun rises north of east (south of east for
southern hemisphere), peaks out nearly overhead, and sets north of west (south of west for southern hemisphere). During the
winter months, the sun rises south of east (north of east for southern hemisphere), peaks out at a low angle above the southern
horizon (northern horizon for the southern hemisphere), and sets south of west (north of west for southern hemisphere). On
the equinoxes, the sun rises due east and sets due west (Figure 2).
9

Figure 2 - Sun’s annual movement. Source - www.nuffieldfoundation.org
1.3.3. Sun position terminology
For the purpose of solar design, the sun’s path and position on four key days out of the 365 days a year, are usually sufficient
– the two solstices and the two equinoxes. The summer solstice (usually occurs between June 20 and June 22 for the northern
hemisphere) has the longest day of the year, and the winter solstice (December 20 – 22) has the least. On the equinoxes
(March 21 and September 21) there are exactly 12 hours of day and night. These four days represent the maximum,
minimum, and inflection points for the angles used to define the position of the sun: azimuth and altitude.
The azimuth angle θ, also called the bearing angle, is the angle between the sun and the north-south axis in a plan view of the
site, typically measured in degrees clockwise from the north. Other conventions of measuring the solar azimuth include

9
Ralph L. Knowles, Sun rhythm form (Cambridge, Mass: MIT Press, 1981), 52-53.
14

measuring east or west from the south, where degrees due east are considered positive and those due west as negative, or vice
versa
10
. This investigation measures azimuth in degrees clockwise from the north.
The azimuth defines at what direction the sun is at a given time of the day. Because of sun’s continuous movement
throughout the day, this angle is different for different times of the day. This angle is symmetrical about the north-south axis
at sunrise and sunset for a day. On the equinoxes, the solar azimuths at sunrise and sunset are 90° and 270° respectively.
11

The altitude angle α, is a measure of how high the sun is in the sky for a given day. It is the angle the sun makes from the
horizon, measured in degrees. It is zero at sunrise and sunset and highest at noon. It is also referred to as the elevation angle.
The altitude angle is 0° at sunrise and sunset, and 90° when the sun is directly overhead (Figure 3).
12

Altitude and azimuth can be calculated by the following equations:
13

𝑠𝑖𝑛 𝛼 = 𝑐𝑜𝑠 𝐿 𝑐𝑜𝑠 𝛿 𝑐𝑜𝑠 𝐻 + 𝑠𝑖𝑛 𝐿 𝑠𝑖𝑛 𝛿
cos 𝜑 =
sin 𝛿 − sin 𝛼 sin 𝐿 𝑐𝑜𝑠 𝛼 . cos 𝐿

Where:
α = altitude angle,
φ = azimuth angle,
L = site latitude, in degrees north or south of the equator,
H = hour angle
δ = declination angle

Figure 3 - Altitude and azimuth of the sun. Source - www.wiki.naturalfrequency.com
The solar hour angle H describes the angular distance between the sun’s current positions to its peak at noon. The hour angle
converts the local solar time (t) into the number of degrees which the sun moves across the sky. As per definition, the hour
angle is 0° at solar noon. The earth rotates 15° per hour. This implies that each hour away from the solar noon corresponds to
an angular movement of 15° of the sun across the sky. Before noon the hour angle is negative, and after noon the hour angle
is positive (Figure 4).
14

Hour angle is given by the following equation –
Hour angle H = 15° (12 - t)

10
"Azimuth Angle." Azimuth Angle. Accessed August 30, 2015. http://www.pveducation.org/pvcdrom/properties-of-
sunlight/azimuth-angle
11
Ibid.
12
"Elevation Angle." Elevation Angle. Accessed August 30, 2015. http://www.pveducation.org/pvcdrom/properties-of-
sunlight/elevation-angle
13
"The Sun's Position." The Sun's Position. Accessed August 31, 2015. http://www.pveducation.org/pvcdrom/properties-of-
sunlight/suns-position
14
Ibid.
15

Where, t = Local Solar Time.

Figure 4 - Hour Angle. Source - www.appropedia.org
The Local Solar Time t is a means of reckoning the time based on the sun’s position. It varies from the local time because of
the eccentricities of the Earth’s orbit and human adjustments such as time zones and daylight saving. For example, twelve
noon local solar time is defined as when the sun is highest in the sky, which may or may not corresponding to 12 noon local
time. The solar time is unique to each particular longitude. The local solar time is important because azimuth and altitude, the
two angles used to define sun’s position at any time of the day, are calculated based on the local solar time and not the local
time.
15

Local solar time is given by,
𝑡 = 𝐿𝑇 +
𝑇𝐶
60

Where,
LT = Local time
TC = Time Correction factor.
The Time Correction Factor TC (in minutes) takes into account the difference between the local time and the local solar
time.
16
This is given by,
TC = 4(Longitude – LSTM) + EoT
Where,
LSTM = Local Standard Time Meridian
Longitude = site longitude in degrees, positive east of the Prime Meridian and negative west of the Prime Meridian.
EoT = Equation of Time
The factor of 4 minutes comes from the fact that the Earth rotates 1° in 4 minutes.
The Local Standard Time Meridian (LSTM) is a locally chosen reference meridian specific to a particular time zone and is
similar to the Prime Meridian, which is used for Greenwich Mean Time.
17
It is defined as,
LSTM = 15°. ∆T GMT
Where ΔT GMT is the difference of the Local Time (LT) from Greenwich Mean Time (GMT) in hours.
The 15° accounts for Earth’s hourly rotation, which is 15° per hour.

15
"The Sun's Position." The Sun's Position. Accessed August 31, 2015. http://www.pveducation.org/pvcdrom/properties-of-
sunlight/suns-position
16
Ibid.
17
Ibid.
16

The Equation of Time EoT (in minutes) describes the discrepancy between the solar time and the local time. It is an empirical
equation that corrects for the eccentricity of the Earth's orbit and the Earth's axial tilt.
18
It is given by,
𝐸𝑜𝑇 = 9.87 sin(2𝑑 ) − 7.53 cos 𝑑 − 1.5 sin 𝑑
Where 𝑑 =
360
365
(𝑛 − 81) , n is day of the year. For January 1, n = 1, and so on.
Solar Declination δ is the angular position of the sun (at solar noon) with respect to the plane of the equator. The angle varies
seasonally due to the tilt of the Earth on its axis of rotation and the rotation of the Earth around the sun. The Earth’s axis has
a tilt of 23.45°, and the declination angle varies plus or minus this amount
19
. Declination can be calculated for a given day
using:
δ = 23.45 sin [360 (284 + n) / 365]
Where n is day of the year. For January 1, n = 1, and so on.
Declination on summer solstice is 23.45°, 0° on both the equinoxes, and -23.45° on winter solstice (Figure 5).

Figure 5 - Solar declination angle ( δ) throughout the year. As the earth orbits around the sun, the angle between the earth’s
equatorial plane and orbital plane varies from -23.45° to 23.45°. Source - www.blc.lsbu.ac.uk
1.4. Solar access
The concept of solar access is not new. Civilizations in the past have designed for the sun. Greek colonial cities and early
settlements in the United States were designed for the sun
20
. With increased awareness in sustainable architecture, and the use
of solar energy systems, recent years have seen a growing interest in solar access laws. According to Knowles, assured sun
access is the key to a quality life. He describes the importance of solar access as –
“The sun is fundamental to all life. It is the source of our vision, our warmth, our energy, and the rhythm of our lives. Its
movements inform our perceptions of time and space and our scale in the universe.
Assured access to the sun is thus important to the quality of our lives. Without access to the sun, our perceptions of the world
and of ourselves are altered. Without the assurance of solar access, we face uncertainty and disorientation. We may lose our
sense of who and where we are.”
21

In regards to solar access on an urban level, Knowles believes the use of solar envelopes as a zoning tool could ensure solar
access–
“The worldwide need for solar-access zoning policies is now critical. The use of solar energy in urban buildings is not first
and foremost a technical or architectural problem. In recent years architects have done good passive and low energy design.
However, much of it has been done on isolated buildings, often in rural settings where solar access is not an issue. Rather the
issue becomes critical in cities where, without guaranteed access, individual buildings cannot depend on the sun. Since sixty

18
"The Sun's Position." The Sun's Position. Accessed August 31, 2015. http://www.pveducation.org/pvcdrom/properties-of-
sunlight/suns-position
19
"Declination Angle." Declination Angle. Accessed August 31, 2015. http://www.pveducation.org/pvcdrom/properties-of-
sunlight/declination-angle
20
Ralph L Knowles, The solar envelope. Solar Law Reporter. 1980; 2(2):263.
21
Ralph L. Knowles. "The Solar Envelope." The Solar Envelope. Accessed October 28, 2015. http://www-
bcf.usc.edu/~rknowles/sol_env/sol_env.html
17

percent of the world’s people are expected to occupy cities by 2030, how urban buildings use energy will determine how most
energy will be used in the world. We know how to make solar buildings. We need to learn how to make solar cities. By using
a concept of solar zoning called solar envelope, we can address issues of a right to sunshine in cities for energy and life
quality.”
22

1.4.1. Precedents
The idea of solar access can be seen at least 3000 years ago in the ancient Greek colonial cities. These cities had gridiron
plans, which were so arranged that all the houses faced the sun for heat and light. The city of Olynthus had such a typical
arrangement, where residential blocks were set along the east-west axis. Each block typically had ten houses, five on each
long side of the block (Figure 6).
23

Figure 6 - The Greek planners of Olynthus arranged houses to have two fronts: one to the sun and one to the street. The
diagram shows the approximate location of south-facing courtyards centering each house. (North, up.). [Image and caption
courtesy – Ralph Knowles]
Although the houses varied in size, each had a south-facing courtyard. This resulted in each house having not just a street
front, but also a “sun – front”. Houses facing south to the street and the sun were designed to have the entrance through the
courtyard. Houses that faced north to the street, were entered through the main body of the building, with passageways
leading to the south facing courtyard.
24

Ancient settlements in North America also provided for solar access. Acoma Pueblo, located on a high-desert plateau about
60 miles from Albuquerque, NM is an example of such early planning.
25

This settlement consists of terraced houses generally facing south. The walls are of thick masonry and roofs and terraces are
of timber and reeds, overlaid with a mixture of clay and grass. The houses were designed such that the low winter sun rays
strike most directly the south facing walls. The thick masonry stores up the sun’s heat during the day and releases it at night
so as to keep the internal spaces comfortable at night. During the summer, the sun strikes the roof, which being constructed of
low thermal mass materials, do not store heat.
26

Mostly importantly, however, the spacing between two rows of houses is such that they do not overshadow each other during
the winter months, thus enabling the sun to heat up each house passively (Figure 7).
27

Figure 7 - Acoma Pueblo. Thick masonry walls and timber roof-terraces respond well to seasonal migrations of the sun
(left). The spacing between Acoma's rows of houses is strategic: just far enough to avoid winter shadows while conserving
precious space on a high, small plateau (right). [Image and caption courtesy – Ralph Knowles]

22
Ralph L. Knowles, Karen M. Kensek “The Growing Need for Solar Access Zoning” (paper presented at the Proceedings of
the 2005 Solar World Congress, Orlando FL, 2005).
23
Donald Watson: Time-Saver Standards for Urban Design. The solar envelope, Chapter (McGraw-Hill Professional, 2003),
AccessEngineering
24
Donald Watson: Time-Saver Standards for Urban Design. The solar envelope, Chapter (McGraw-Hill Professional, 2003),
AccessEngineering
25
Ralph L Knowles, The solar envelope. Solar Law Reporter. 1980; 2(2):263.
26
Ibid.
27
Ralph L Knowles, The solar envelope. Solar Law Reporter. 1980; 2(2):263.
18

Cave dwellers of Longhouse, Mesa Verde, CO, also adapted for the sun. These settlements were located within a large
southwest facing cave. The dimensions of the cave is such that the brow of the cave blocks the high angle summer sun, but
lets in the low angle winter sun into the inside of the cave. The dwellers of Mesa Verde also moved in and out of the cave
seasonally. During summer, they tended to stay near the back of the cave, where the sun did not reach and the high thermal
mass of the cave walls ensured a cool space. During winter months, the dwellers would move south, into the open terraces
where the sun was shining (Figure 8).
28

Figure 8 - The winter sun angles reach deep into the cliff dwellings at Mesa Verde, while the summer rays are blocked by the
overhanging cliff. [Image and caption courtesy – Ralph Knowles]
1.4.2. Solar access zoning
Solar access zoning refers to regulations which are intended for the protection of access to the sun on a site or a building.
29

This is also known as “right to light”. In his paper, “The Solar Envelope - Its Meaning for Urban Growth and Form,”
30

Knowles describes the growing importance of solar access in the United States, and the need for legal framework for solar
access as –
“Solar access has, over the past twenty-five years, come into focus as a topic of discussion in the United States. Beginning in
the 1970's, communities looked at the sun primarily as a source of energy, a replacement for uncertain supplies of fossil fuel.
Then, during the 1980’s, interest in solar access generally abated as oil supplies became more reliable. But most recently,
even though oil is now plentiful and cheap, environmental concerns are causing a renewed interest in sun rights as a
condition of sustainable growth and life quality. Solar access thus remains today a legitimate area of public policy in which
the aim is to regulate how and when neighbors may shadow one another.”
The most prevalent method to ensure solar access is via a solar easement. A land owner also has property rights over the air
space above their plot of land, regardless of if they build up. Because of this, the land owner has the right to grant an
easement for light within the air space. Other ways to address solar access legally, is through land use planning and policy
making. This can be done by incorporating solar site planning, which allows developers to maximize southern exposure for
solar access. By efficiently placing trees, major vegetation and other tall buildings solar access to residential buildings can be
maximized. Policies such as solar easements can be used in this case.
31

One of the earliest right to light laws is The Doctrine of Ancient Lights in England. This is a negative easement law, which
states that an adjoining structure cannot block to right to light of an existing structure. If a landowner has received
unobstructed sunlight for a period of time, they have the right to continue receiving for all time. Thus, a building owner with
such an easement can block a development if it blocks their solar access.
32

In a 1939 court case, Lynch v. Hill (24 Del.Ch. 86, 6 A.2d 614), brought to the Delaware Court of Chancery, set a precedent
that the English Doctrine of Ancient Lights has no standing in the United States and that property owners have no rights to

28
Donald Watson: Time-Saver Standards for Urban Design. The solar envelope, Chapter (McGraw-Hill Professional, 2003),
AccessEngineering
29
Ralph L. Knowles, Sun rhythm form (Cambridge, Mass: MIT Press, 1981), 10.
30
Ralph L. Knowles. "The Solar Envelope: Its Meaning for Urban Growth and Form." Architecture - City - Environment,
Proceedings of PLEA 2000, 2000, 649-54.
31
Colleen McCann Kettles. "A Comprehensive Review of Solar Access Law in the United States - Suggested Standards for a
Model Statute and Ordinance." Solar America Board for Codes and Standards. October 1, 2008. Accessed October 27, 2015.
http://www.solarabcs.org/about/publications/reports/solar-access/pdfs/Solaraccess-full.pdf.
32
Alicyn E. Henkhaus, “Computer-Generated Solar Envelopes and Building Information Modeling (BIM)” (master’s thesis,
University of Southern California, 2012), 13.
19

easements based on the right to light. Many cases upheld this precedent, and in 1959 in the Fontainebleau Hotel Corp. v.
Forty-Five Twenty-Five, Inc. (114 So. 2d 357, 1959 Fla. App. LEXIS 2744), where a new addition to a hotel in Miami,
Florida, would overshadow the pool area and the beach area of a neighbouring hotel, the judges were of the opinion that as
the Doctrine of Ancient Lights was repudiated nationwide, it would not be upheld in this case. In the end, however, the
judges ruled against the addition, as the addition would “materially damage” the other property, but there were no legal
protection of the right to light of properties, both in the local ordinances of the City of Miami and previous American court
decisions.
33

There are no national laws or policies to protect the right to light of property owners in the United States. There are, however,
a number of local ordinances and planning policies which have legal protection of right to light, to various degrees. These
municipalities include San Francisco, CA; Santa Barbara, CA; Santa Cruz County, CA; Boulder, CO; Fort Collins, CO; New
York City, NY; Ashland, OR; and Clackamas County, OR, among others.
34

1.4.3. California Solar Rights Act
The California Solar Rights Act was created in 1978 (AB 3250, 1978), and it created a legal framework for solar access. The
law provides protections and allows building owners access to sunlight and prevent shading of solar energy systems such as
photovoltaic panel and solar water heater systems. The provisions of the Act limits agreements, conditions or restrictions
which are typically imposed by homeowner associations and local governments from preventing installation of solar energy
systems. The Act also has provisions for legal rights to solar easement.
35

The main purpose of the Solar Rights Act was to promote and encourage the widespread use of solar energy systems. This
law came into effect at the time of oil shortage and energy crisis in the United States. As a result of the crisis, emphasis was
placed on solar energy systems and other renewable energy sources. This law sought to "protect and facilitate adequate
access to the sunlight which is necessary to operate solar energy systems." The Solar Rights Act, despite being about 30 years
old, still holds relevance, and contributes towards California’s commitment to solar energy. The rationale of the Act is still
relevant today, and supports California’s solar energy policies.
36

While the Act protects building owners’ rights to install solar energy system, protection of access to sunlight is not provided.
Some local governments have local ordinances to augment the law and add protection of solar access for building owners,
such as the City of Santa Barbara (Santa Barbara Ordinance #4426, 7 Oct 1986; Santa Barbara Municipal Code Chapters
28.11, 28.15, 28.18, 28.21, 28.92)
37

The California Solar Shade Act (AB 2321, 1978) provides some protection against shading of solar energy systems by trees
and vegetation. The provisions of this law state that a property owner cannot allow any trees or major vegetation to shade the
solar energy systems of a neighbouring property, if the trees were planted after the solar energy device was installed.
38

1.5. Scope of work
The amount of volume that can be added to the existing building geometry without casting additional shadows, using similar
principle as those used to generate solar envelopes has been determined. A solar envelope generation tool has been created in
Dynamo, to work with Revit, based on user input. Parameters considered for this tool were site location (latitude and
longitude), envelope cut-off times, site grid orientation, and shadow fence. Due to time constraints non-rectangular sites and
sites on a slope were not considered.
To test out the hypothesis, two building geometries were tested – a rectangular geometry, and an L-shaped geometry in
different orientations. The site location (latitude and longitude) and envelope cut-off times were varied in each case, solar
envelopes for the whole sides of the building were generated, and the increase in building volume was calculated and
compared.

33
Alicyn E. Henkhaus, “Computer-Generated Solar Envelopes and Building Information Modeling (BIM)” (master’s thesis,
University of Southern California, 2012), 13-14.
34
Alicyn E. Henkhaus, “Computer-Generated Solar Envelopes and Building Information Modeling (BIM)” (master’s thesis,
University of Southern California, 2012), 14.
35
"Solar Rights: Access to the Sun for Solar Systems." Rights to the Sun - Go Solar California. Accessed October 28, 2015.
http://www.gosolarcalifornia.ca.gov/solar_basics/rights.php.
36
Ibid.
37
Alicyn E. Henkhaus, “Computer-Generated Solar Envelopes and Building Information Modeling (BIM)” (master’s thesis,
University of Southern California, 2012), 15.
38
"Solar Rights: Access to the Sun for Solar Systems." Rights to the Sun - Go Solar California. Accessed October 28, 2015.
http://www.gosolarcalifornia.ca.gov/solar_basics/rights.php.
20

Next, to determine practical applications of results, they were applied to a commercial zone in Los Angeles. The increase in
floor area ratios by building within the solar envelope geometry, from the existing floor area ratios, without further impacting
solar access of the buildings was calculated.
1.6. Application of work
Knowing how much more can be added to the existing building geometry without casting additional shadows can have the
following possible practical applications –
1. Such information could be part of zoning ordinances, controlling additions and renovations to existing buildings not
built within a solar envelope, to prevent additional shadows being cast as a result of additions.
2. Conversely, these principles could be used by existing buildings to make renovations and additions to the building
geometry, without further impacting the solar access of the surrounding buildings.
3. If the volume added is large enough, extra floor area can be added in existing buildings. This would increase
rentable space of the building.
4. With this information, buildings can now easily install PV systems without fearing overshadowing by later additions
to surrounding buildings.
21

CHAPTER 2
2. BACKGROUND
This chapter has two parts. Part 1 describes research done on conceptualization and generation of solar envelopes, and the
factors involved that affect solar envelopes. Part 2 details existing solar envelope tools and solar envelope tool making
techniques.
PART I
2.1. The solar envelope
The solar envelope for a site is the largest volume that can be built without casting shadows onto the neighbouring buildings
for a certain time of the day. This concept of solar envelopes was conceived and tested by Prof. Ralph Knowles, working
with Prof. Richard D. Berry, at the University of Southern California, School of Architecture between 1969 -71. In 1977, as a
part of an undergraduate studio, directed by Knowles and Berry, students began to design buildings using solar envelopes.
Working with upper-division undergraduates as a part of “Solar Studio,” Knowles further developed the envelope concept as
an urban zoning policy.
39

Knowles’ research argues that the solar envelope, when used as an urban zoning tool, will not only ensure solar access for all
buildings, but also result in aesthetically pleasing urban forms. Based on his study on the Los Angles zoning, Knowles
showed that using solar envelope based solar access zoning, will not curb high density and high rise development, and floor
area ratios as high as 7.5 and housing densities of more than 100 dwelling units per acre are achievable through solar
envelope zoning.
40

2.2. Solar envelope principles
The solar envelope is constructed of space and time. It is based on two main parameters – the physical boundaries of the site
and the surroundings (space), and the time period during the day, of their access to sunlight (time).
41

The envelope provides the largest volume that can be built without overshadowing within specific time constraints. These are
called the cut-off times. The envelope essentially defines the largest theoretical container of space that would not cast
shadows off site for the specified cut-off times. Solar access requirements have an inverse relationship with site volume: the
more hours of solar access that are required, the smaller the volume of the resulting solar envelope will be.
42

2.3. Generating solar envelopes
The technique to generate solar envelope described in this section was developed by Ralph Knowles, as explained in his
book, Sun Rhythm Form.
43
This example considers a rectangular site, oriented east-west. The limits of the solar envelope are
determined by the daily and the annual movements of the sun.
The daily movement of the sun from east to west determines the eastern and the western boundaries of the envelope. To
locate these boundaries, the first step is to fix the useful hours of solar access, i.e., the hours during which overshadowing on
the neighbouring buildings is to be avoided. To understand how daily solar movement is used to determine the east and west
boundaries, an imaginary flag is considered to be placed in the middle of the site.
In the early hours of the morning, the shadow from the flag will be cast to the west, and in the late afternoon, to the east. The
upper limits of the envelope slope down from the top of the flag to the edges of the western boundary of the site in the
morning, and to the eastern boundary in the afternoon. This slope is determined by the solar altitude and azimuth at that time.
The actual developable volume is then determined by considering a plane at the centre, parallel to the east-west edges of the
site, instead of the flag, which casts shadow on both directions. Morning shadows cast from the top edge of this plane,
intersects the western boundary, and afternoon shadow intersects the eastern boundary. The resulting combined limits is a
tent-like enclosure, open at the north and south ends. These are the eastern and the western limits of the envelope (Figure 9).

39
Uen-Fang Patricia Yeh. Computer aided solar envelope design (master’s thesis, ProQuest, UMI Dissertations Publishing,
1992).
40
Ralph L. Knowles. "The Solar Envelope: Its Meaning for Urban Growth and Form." Architecture - City - Environment,
Proceedings of PLEA 2000, 2000, 649-54.
41
Ralph L. Knowles, Sun rhythm form (Cambridge, Mass: MIT Press, 1981), 51-52.
42
Ibid, 61.
43
Ibid, 54-56.
22

Figure 9 - – Boundary determination for east and west sides. Source – Sun Rhythm Form - Chapter 3: Solar Envelope of Sun
Rhythm Form (Knowles, 1981 pp.54 -6)
The north and south boundaries of the envelope is determined by the annual movement of the sun. Considering the same
imaginary flag as before, the winter sun casts a shadow of the flag towards the north. The summer sun, which is higher in the
sky, and more towards the northern horizon, casts a shadow towards the south of the flag.
The winter shadows delineate the northern boundaries of the envelope, and the summer shadows define the southern
boundary. The resulting enclosure is tent like, open at the east and the west ends. As the winter sun has a lower altitude, the
northern boundary has a gentler slope than the southern one. The summer sun, being quite high in the sky, results in a steeper
slope on the southern side (Figure 10).

Figure 10 - Boundary determination for north and south sides. Source – Sun Rhythm Form - Chapter 3: Solar Envelope of
Sun Rhythm Form (Knowles, 1981 pp.54 -6)
To generate the solar envelope, the next step is to integrate the two enclosures created above. The resulting shape is a
prismatic geometry, sloping down from a ridge point on all four sides (Figure 11).

Figure 11 – The complete envelope. Source – Sun Rhythm Form - Chapter 3: Solar Envelope of Sun Rhythm Form (Knowles,
1981 pp.54 -6)
This process describes the envelope generation for simple rectangular site. More complex envelopes can also be generated for
irregular sites, sloping sites, orientation, and for irregular cut-off times, using similar principles (Figure 12).
23

Figure 12 – Complex solar envelopes. Source – Sun Rhythm Form - Chapter 3: Solar Envelope of Sun Rhythm Form
(Knowles, 1981 pp.54 -6)
2.4. Factors affecting solar envelope geometry
There are several factors which influence the shape of the solar envelope. These are essentially the factors that are used to
specify the conditions of the two main parameters, namely space and time. The physical boundaries of the site and the
surroundings (space) are determined by the shape of the site and the site dimensions, the site slope, and the orientation of the
site.
44

The temporal parameters are based off the sun’s daily and annual movement. Factors which define the sun’s movement affect
the shape of the envelope. These include the latitude and longitude, and the desired cut-off times. Varying each of these will
result in different envelope geometry.
45

2.4.1. Site dimensions
Sites with different sizes which have similar proportions will have solar envelopes of different sizes but similar proportions,
given that the other constraints remain the same. Thus, doubling the edge of a site will double the envelope height, and a
doubling of plan dimensions will double the ridge length. Increasing the size of the envelope decreases the surface to volume
ratio of the envelope (Figure 13).
46

Figure 13 - Solar envelope varying with site dimensions. Source - Sun Rhythm Form - Chapter 3: Solar Envelope of Sun
Rhythm Form (Knowles, 1981 pp.65)

44
Ralph L. Knowles, Sun rhythm form (Cambridge, Mass: MIT Press, 1981), 65-71.
45
Ibid.
46
Ibid.
24

Varying the shape of the site will also have an impact on the solar envelope geometry, even when other factors remain the
same. The ridge of the solar envelope is generally parallel to the longer site edge. With non-rectangular sites, the envelope
geometry becomes more complex.
47

A site having longer north south edge will have its envelope ridge running north-south as well. The solar envelope height in
this case will be determined by the east-west (daily) migration of the sun. For a site with longer east-west edge, the envelope
ridge will run east-west. The solar envelope height in this case will be determined by the north-south (seasonal) migration of
the sun.
48

2.4.2. Site orientation
The street grid also affects the shape and size of the solar envelope. Two types of street grids are typical in the United States
– the Jeffersonian grid and the Spanish grid. The Jeffersonian grid has streets running along the cardinal directions, so that
rectangular blocks extend east-west and north-south of the grid. Knowles maintains that the Spanish grid is based off the
climate and the topography. Streets run at roughly 45 degrees from the cardinal directions. This grid is typical in Los
Angeles’ older part and is based off the direction of sea breezes. The solar envelope’s geometry is influenced by the typical
shadow patterns of the different street grids.
49

Streets that run east-west will tend to be shadowed during all of a winter day, whereas streets that run north-south are sunlit
during the peak daytime, and are consequently more pleasant to use during the day. On the other hand, in summer, streets
running the east-west direction will receive little shadow at midday, and much less during the morning and the afternoon.
Streets that run north-south will be shaded morning and afternoon, but will be under the sun at midday. Thus, the Jeffersonian
grid have too dark east-west streets in the winter, and too bright north-south streets in the summer.
50

The Spanish grid has more advantages when it comes to light and heat. All streets receive direct light and heat from the sun
sometime between 9 am and 3 pm, which are the critical hours. In the summer, every street is shaded at most parts during
most of the summer day (Figure 14).
51

Figure 14 - Shadow patterns for different street orientation. Source - Ralph Knowles - Sun, Rhythm Form, MIT Press 1981
Street orientation affects solar envelopes in two ways. It affects the amount of developable volume of the envelope, as well as
the general urban design.
52

In terms of urban design, street orientation affects urban legibility. Using solar envelopes as a framework for urban
development can increase urban legibility by making urban orientation more clear.
53

The solar envelope for a city block oriented along the cardinal points will have a higher envelope height and a larger
developable volume than a block oriented diagonally. Thus, with the Jeffersonian grid, more envelope volume is possible
than with the Spanish grid. Within the Jeffersonian grid, blocks that run long in the east-west direction have the most
envelope volume and the highest ridges, more than blocks that run north-south. In this case, development will occur

47
Ralph L. Knowles, Sun rhythm form (Cambridge, Mass: MIT Press, 1981), 65-71.
48
Ibid.
49
Ibid, 20-23.
50
Ibid.
51
Ibid.
52
Ibid.
53
Ibid.
25

symmetrically along the short dimension of the block, and asymmetrically over the long side, with higher buildings on the
north, and lower on the south to allow winter sun (Figure 15).
54

For blocks that run north-south, the ridge will run lengthwise down the middle of the block. Such a development will be
symmetrical on the north and south sides, while the shorter east-west streets will be higher on the north, and lower on the
south (Figure 15).
55

The Spanish grid will have the smallest envelope volume. The ridge will run along the southeast boundary, and all streets will
be developed asymmetrically. The northwest and the northeast sides will be higher, and the southwest and southeast sides
will be lower to let in winter sun. Intersections will have a higher building on the north corner, and shorter ones at the other
three corners (Figure 15).
56

Figure 15 - Three different block orientations demonstrate the effect on size and shape of solar envelopes. Image - Ralph
Knowles, Sun Rhythm Form, MIT Press, 1981
If a site is not oriented along any of the grids specified, solar envelope size is dependent on its angle of orientation. With an
angular rotation of the site, the total envelope volume and the height of the ridge will decrease (Figure 16).
57

Figure 16 - – Solar envelope varying with grid orientation. Source - Sun Rhythm Form - Chapter 3: Solar Envelope of Sun
Rhythm Form (Knowles, 1981 pp.65 -71)
2.4.3. Site slope
Both the height and the volume of the solar envelope are affected by the slope of the site. If the site dimensions are kept
constant and vary the slope, the envelope height will change. Beginning with a flat site, as we increase the slope towards the
south, the height, and therefore the volume, of the envelope increases. As the slope approaches the vertical, however, the
volume decreases. If, instead, the height of the envelope is maintained at a constant value, a gradual increase of slope will
result in smaller site dimensions in the north-south directions, and therefore, smaller volumes (Figure 17).
58

54
Ralph L. Knowles, Sun rhythm form (Cambridge, Mass: MIT Press, 1981), 20-23.
55
Ibid.
56
Ibid.
57
Ibid, 70-71.
58
Ibid, 68-69.
26

Changing the orientation of the fixed slope also impacts solar envelope volume. Sites on south facing slopes (equator-facing
slope) will generally have envelopes with larger volumes and height than those facing north (non-equator facing). Envelopes
on east and west slopes are dependent on the site shape, but they generally contain moderate height and volume. If the height
of the envelope is kept constant and the orientation varied, the shape of the envelope changes. On south facing slopes, the
envelope’s southern face will elongate and the northern face will shorten. It the reverse for sites on the northern slopes – the
northern face will elongate and the southern face will foreshorten.
59

Figure 17 - – Solar envelope varying with slope. Source - Sun Rhythm Form - Chapter 3: Solar Envelope of Sun Rhythm
Form (Knowles, 1981 pp.65 -71)
2.4.4. Latitude
Altitude also affects the envelope height, and therefore the volume. For the same site, varying the latitude will change the
envelope height. Keeping the cut-off times and the site dimensions the same, sites at latitudes closer to the equator will have
larger height and volume, and those away from the equator will have smaller heights and volumes, because the sun is usually
at a higher angle as one moves closer to the equator, and lower when one moves away from the equator (Figure 18).
60

Figure 18 – Solar envelope varying with latitude. Source - Sun Rhythm Form - Chapter 3: Solar Envelope of Sun Rhythm
Form (Knowles, 1981 pp.65 -71)
2.4.5. Cut-off times
Cut-off times also affect envelope volume. The earlier the cut-off times begin in the morning, and the later they go into the
afternoon, the smaller the envelope height, and volume is. This is because the sun angles are much lower in the early morning
and late afternoon, and much steeper near midday, at all seasons throughout the year. Therefore, the longer the period of solar
access required the smaller the volume of the envelope constructed (Figure 19).
61

Figure 19 - Solar envelope varying with cut-off times. Source - Sun Rhythm Form - Chapter 3: Solar Envelope of Sun Rhythm
Form (Knowles, 1981 pp.65 -71)

59
Ralph L. Knowles, Sun rhythm form (Cambridge, Mass: MIT Press, 1981), 68-69.
60
Ibid, 65.
61
Ibid, 61.
27

2.5. Shadow fence
Many communities have the concept of a privacy fence on the site boundary. This implies that the fence will be casting
shadow, hence these are called shadow fences. When using solar envelopes as a means of solar access in a neighbourhood,
the shadow cast by these privacy fences are the only acceptable shadows.
Integrating the fence as a part of the solar envelope for a site will add to the volume of the envelope, and still provide solar
access for the same specified period of the day. This envelope will now start at the height of the fence from the ground
(Figure 20).
62

Figure 20 - Solar envelope varying with shadow fence. Source - Sun Rhythm Form - Chapter 3: Solar Envelope of Sun
Rhythm Form (Knowles, 1981 pp. 105)
PART II
2.6. Computer aided solar envelope generation techniques
There are mainly three different ways to generate solar envelopes using computer programs. The first, grid and flag pole
method, is a numerical method that involves dividing the site into a grid The second, cutting solids, works with any shaped
site and any topographical conditions, and the third, Boolean intersection, can be used with any program that does that
operation.
63

2.6.1. Grid and Flag Pole
In this technique, the site is overlaid with a grid. At every grid intersection the maximum height of a vector normal to the site
(a “flag pole”) is calculated for each solar access constraint. For each grid intersection the lowest height in the set of
generated flag poles is chosen. The set of lowest heights is then meshed to create the solar envelope. The resulting solar
envelope is an approximation of the actual envelope, and accuracy increases as the resolution of the grid used for calculation
increases. A finer mesh will produce a more accurate envelope.
64

2.6.2. Cutting Solids
In this technique, the site boundary is extruded and volumes that would cast a shadow on the neighbouring buildings are
removed from the extrusion, revealing the final solar envelope volume. The first step in this technique, is the extrusion of the
site boundary, which can be polygonal, and not necessarily rectangular. For each solar access constraint, a vector defined by
the solar azimuth and altitude is defined, and placed at site vertex of the site boundary. A plane comprising of each segment
of the side boundary and the vectors at adjacent vertices is constructed. This plane is then extruded, and cuts away the site
boundary extrusion to create the solar envelope.
65

2.6.3. Boolean Intersection
In this technique the site base is extruded along a vector from the site to the sun for each solar access constraint. Each of these
extrusions is a skewed prism. The envelope is generated by a Boolean intersection of these prisms, i.e., only those points in

62
Ralph L. Knowles, Sun rhythm form (Cambridge, Mass: MIT Press, 1981), 105.
63
Alicyn E. Henkhaus, “Computer-Generated Solar Envelopes and Building Information Modeling (BIM)” (master’s thesis,
University of Southern California, 2012), 24.
64
Alicyn E. Henkhaus, “Computer-Generated Solar Envelopes and Building Information Modeling (BIM)” (master’s thesis,
University of Southern California, 2012), 24-25.
65
Ibid, 25.
28

space are considered which are included within all the prisms. Programs that can perform Boolean intersections can use this
technique.
66

2.7. Previous solar envelope generating tools
A lot of work has been done over the years to create computer tools to generate solar envelopes. However, none of them
work with a BIM software, like Revit. Part of the objective of this thesis is to create a solar envelope generation tool for a
BIM program. This section describes some of the existing solar envelope generation software.
2.7.1. SolCAD
This tool was developed by Manu Jayal and Karen Kensek at USC School of Architecture. This tool can generate complex
solar envelopes, and is compatible with CAD programs such as AutoCAD and form_Z. This program is written in Java
programming language and uses Java3D library for graphics display. The user draws the site boundaries in AutoCAD, which
is then exported as a DXF file, and the solar envelope is constructed in SolCAD. Two types of envelopes can be constructed
– a single day envelope for a specific day, and a composite envelope for different days of the year or the whole year. This
program uses the grid and flag pole method for solar envelope generation. The site is overlaid with a grid. At every grid
intersection the maximum height of a vector normal to the site (a “flag pole”) is calculated for each solar access constraint.
For each grid intersection the lowest height in the set of generated flag poles is chosen. The set of lowest heights is then
meshed to create the solar envelope. It also allows users to analyse courtyards, and different heights for shadow fences on the
neighbouring sites (Figure 21).
67

Figure 21 - Envelope generation in SolCAD. [Image courtesy – Manu Juyal.]
2.7.2. SolVelope
This tool was developed by Uen-Fang Patricia Yeh in 1992 at USC with Marc Schiler as her adviser. The technique used for
this tool is the grid and flagpole techniques for solar envelope generation. In this program, the site is overlaid with a grid. At
every grid intersection the maximum height of a vector normal to the site (a “flag pole”) is calculated for each solar access
constraint. For each grid intersection the lowest height in the set of generated flag poles is chosen. The set of lowest heights is
then meshed to create the solar envelope. It was written in BASIC. User input included site information, latitude, and the cut-
off times for solar access. The program is not connected to any CAD program.
68

2.7.3. CalcSolar
This was developed by Karen Kensek at the USC School of Architecture in 1995 using AutoLisp. Unlike SolVelope, this tool
was connected to AutoCAD, and all user inputs, calculations and results could be viewed in AutoCAD. Site boundaries and
solar access constraints are drawn in AutoCAD by the user, and additional inputs are entered as numerical values. The final
output is displayed in AutoCAD as a surface model, which can also be exported for use in other CAD programs as a DXF

66
Alicyn E. Henkhaus, “Computer-Generated Solar Envelopes and Building Information Modeling (BIM)” (master’s thesis,
University of Southern California, 2012),, 26.
67
Manu Juyal, SolCAD: Three-dimensional spatial design tool to generate solar envelope (Master’s thesis ProQuest, UMI
Dissertations Publishing, 2002.)
68
Uen-Fang Patricia Yeh. Computer aided solar envelope design (master’s thesis, ProQuest, UMI Dissertations Publishing,
1992).
29

file. In addition, it also allows different heights for shadow fences around neighbouring sites and analysing courtyards. It also
uses the grid and flagpole technique.
69

2.7.4. DIVA for Rhino
DIVA for Rhino is a component for the Grasshopper plug-in to Rhino. Recent releases of the DIVA plug-in include a solar
envelope generator. Solar envelopes are generated using the Boolean intersection technique. The site base is extruded along a
vector from the site to the sun for each solar access constraint. Each of these extrusions is a skewed prism. The envelope is
generated by a Boolean intersection of these prisms, i.e., only those points in space are considered which are included within
all the prisms. Four extrusions are used to calculate the solar envelope. All extrusions share the same base. There is one
extrusion for each of the two cut-off times (morning and evening) on both the summer and winter solstice. The planar
boundary is extruded along a vector defined by the solar azimuth and altitude at each of the four constraints.
70

2.7.5. Right to Light in Ecotect
This tool is based on UK’s specific right-to-light guidelines produced by the Building Research Establishment (BRE). This
tool works on the rule that that a building will have the potential for good interior diffuse daylighting if there are no
obstructions above a 25 degree cut-pane from the horizontal, 2m above the ground.
71

2.7.6. Solar envelope generator for BIM using Revit API
Developed by Alicyn Henkhaus in 2012 along with Karen Kensek, this tool works with Revit. It is a plugin for Revit
architecture, and is written in written in C# for the Revit .NET API. The method of generation followed in this tool is cutting
solids method. The user is required to input site information and solar access requirements. The site geometry is inputted by
reference points placed on each vertex of the site. The site is extruded as a solid, and void solids are generated as solar access
constraints. The extruded site solid is cut-off by the void solids, to generate the final solar envelope.
72

2.8. Chapter summary
The solar envelope for a site is the largest volume that can be built without casting shadows onto the neighbouring buildings
for a certain time of the day. When used as an urban zoning tool, it ensures solar access for everyone. The solar envelope is
constructed of space and time. Space refers to the physical site dimensions, street orientation, and site slope. Time refers to
the site latitude, and the desired cut-off times. Varying these parameters will affect the solar envelope geometry.
Different computer tools have been developed to generate solar envelopes. These tools are mainly based on three different
envelope generation techniques – grid and flag pole, cutting solids and Boolean intersection. Some of the existing solar
envelope tools are SolCAD, SolVelope, CalcSolar, DIVA for Rhino Solar Envelope generator, and Right to Light in Ecotect.

69
Alicyn E. Henkhaus, “Computer-Generated Solar Envelopes and Building Information Modeling (BIM)” (master’s thesis,
University of Southern California, 2012), 28.
70
"Solar Tools." - DIVA for Rhino. Accessed August 31, 2015. http://diva4rhino.com/user-guide/grasshopper/solar
71
"Ecotect: Right to Light and Solar Envelope | Sustainability Workshop." Ecotect: Right to Light and Solar Envelope |
Sustainability Workshop. Accessed August 31, 2015. http://sustainabilityworkshop.autodesk.com/buildings/ecotect-right-
light-and-solar-envelope
72
Alicyn E. Henkhaus, “Computer-Generated Solar Envelopes and Building Information Modeling (BIM)” (master’s thesis,
University of Southern California, 2012), 38-48.
30

CHAPTER 3
3. METHODS
This chapter gives an overview of the methods followed for this investigation. Part I, which describes these methods, deals
with determining ways to generate solar envelopes for sites with existing buildings, and testing out various scenarios to
determine how different factors affect the volume of the envelope generated, followed by applying the principle to an urban
neighbourhood to determine feasibility of the results. Part II of this chapter, describes creating a Dynamo script for
generating solar envelopes.
PART I
3.1. Solar envelope tool generation
For the purpose of studying the effects of solar envelopes for sites with existing buildings, a solar envelope generation tool
was developed using Dynamo’s visual scripting platform, to work with Revit. The size and shape of the solar envelope
depend on various factors, as described in Part I of Chapter 2. This tool takes into account the parameters described and,
based on user inputs, generates a solar envelope.
3.1.1. Dynamo script
Dynamo is a visual scripting program that uses a graphical interface to create parametric forms. It uses computational logic to
generate geometric forms, which was one of the reasons for choosing this program to create the tool. A script was written in
Dynamo to generate solar envelopes. This is described in detail in Part II of this chapter. The algorithm for the tool has been
derived from the solar envelope generation technique described in section 2.3. The script takes in spatial and temporal
information from the user to generate the required solar envelope geometry. Parameters considered for this tool were site
location (latitude and longitude), envelope cut-off times, site grid orientation, and shadow fence. Non-rectangular sites and
sites on a slope were not considered in this phase, and may be examined in future phases of this research.
3.1.2. Test cases
The script takes in user inputs, which include site width and length, site orientation, shadow fence height, the latitude and the
longitude of the site, the time difference from GMT (without daylight saving), and the beginning of the summer and winter
cut-off times. The reason it takes only the beginning of the cut-off times and not the ends, is because it considers the cut-off
times to be symmetrical about noon, hence only the beginning is required.
After the script was running successfully for one test case, it was tested for different situations, such as for different locations
(different latitudes), different cut-off times, and site conditions (different site dimensions, site orientations) (Figure 22, Figure
23, Figure 24).

Figure 22 - Solar envelope generated using the tool - a. Within the cut-off times. b. Outside the cut-off times
31

Figure 23 - Solar envelope generated using the tool, with different site dimension and different location - a. Within the cut-off
times. b. Outside the cut-off times

Figure 24 - Solar envelope generated using the tool, with different grid orientation - a. Within the cut-off times. b. Outside
the cut-off times
3.2. Solar envelopes for sites with existing buildings
The second part of the investigation involved determining how much more can be added to the existing building geometry
without casting additional shadows, using similar principles as those used to generate solar envelopes. To test this, two
building geometries were tested – a rectangular geometry, and an L-shaped geometry in different orientations. The site
location (latitude and longitude) and envelope cut-off times were varied in each case, solar envelopes for the whole sides of
the building were generated, and the increase in building volume was calculated and compared.
3.2.1. Establish test cases
Two building geometries were tested. The building site is rectangular and is the same for all test cases. The site is flat and
measures 205m in the north-south and 150m in the east-west direction. This is the same site dimensions used by Ralph
Knowles for demonstrating solar envelope generation principles for rectangular sites, in Sun Rhythm Form, and thus will be
used to demonstrate solar envelope generation principles for sites with existing buildings. The first building geometry
considered is a rectangular building. This building sits within the site. Five locations with different latitudes were considered
and envelopes generated. Next, for each latitude, three different cut-off times were tested.
The next geometry considered was an L-shaped building, which sits on the same site as before, and has the same building
height. Four test geometries for the L-shaped building were considered. The same parameters for latitude as before were
considered and tested. All four geometries were tested for five different latitudes, but the same cut-off time. The volumes of
the resulting envelopes were calculated and compared. Figure 25 describes the test cases and the parameters for testing.
32

Figure 25 - The five building geometries tested.
3.2.2. Envelope generation
The investigation was carried out using Revit and the Dynamo tool that was created (see Chapter 3, Part II). The test cases
were modelled in Revit as conceptual masses. Solar envelopes were generated using the tool and imported into Revit.
Additional volumes were also modelled in place on to the test cases as conceptual masses.
There are three places on a site with an existing building were additional volumes could be added without adding to the
shadow cast within specified cut-off times. The first place is on the site itself. Considering the site to be an empty one, one
can build as much as allowed by the solar envelope for that site within the specified cut-off times. If the building footprint
does not occupy the whole site, the remaining portions of the site (not occupied by the building) can be built up to the height
specified by the solar envelope for that site.
Using the Dynamo tool, the solar envelope for the site was generated. This was then imported into Revit, as a conceptual
mass, and added on to the test case model (Figure 26).

Figure 26 - The first place to add additional volume. Anything built within the solar envelope for the empty site will not cast
additional shadows. If the building occupies the whole site, this addition is not possible.
The second place where additional volumes can be added in on the building roof. If the roof is considered as a site, and using
the roof dimensions as site dimensions, and the same specified cut-off times as before, a solar envelope is generated and
placed on the roof, anything built within this volume will not cast any additional shadows. This can also be thought of as a
site with the same dimensions as the building roof, and a shadow fence the same as the height of the building.
Using the Dynamo tool, the solar envelope as defined was generated. This was then imported into Revit as a mass, and placed
on to the building roof of the test model (Figure 27).
33

Figure 27 - The second place to add volume - on the roof. The roof can be considered as a site itself, and a corresponding
envelope be generated for the same.
The third place to insert more volume without casting extra shadows would be on the building sides. Such a volume could be
added within the shadows already being cast by the building. If the extra volume can be “hidden” within the shadow footprint
of the building, then this volume will not be casting additional shadows. So, if during the cut-off times, the building casts
shadows, such that sides of the building is always under shadow, new volumes could be added on to those sides. If within the
cut-off times, the building casts shadows only on one side of the building (regardless of which side), only then can extra
volume be added to the side that is always under shadows, without casting additional shadows (Figure 28).

Figure 28 – Conditions for adding volume to building sides.
Once the sides which are completely under shadow within the cut-off, are determined, the shadow “volumes” being cast at
the beginning and end of the cut-off times are determined. This is done by joining the vertices of the shadow footprint to the
corresponding vertices of the sides casting the shadow. Then, the shadow “volume” at solar noon is determined. The
intersection of these three volumes gives the solar envelope for the sides. A similar procedure is followed for the winter
shadow “volumes” cast. The winter volumes intersect the summer envelope, and the final envelope is generated (Figure 29).
If the volume generated exceeds the site boundaries, then the site boundaries act as an additional constraint, and the volume is
“chopped off” at the boundary, by an imaginary vertical plane at the boundary.
Once the three volumes are developed, they are to be combined to generate the complete solar envelope for the building
(Figure 30). It is to be remembered that although the solar envelope geometry is case specific, and will vary with different
scenarios, the steps to generate it remains the same.
34

Figure 29 - Steps to generate solar envelope for the sides of the building.

Figure 30 - The complete envelope generation.
3.3. Urban Application
The third part of the investigation examined the feasibility of the results obtained from the study of the test cases. For this
purpose, the principles were tested out in a neighbourhood in downtown Los Angeles. The purpose of this exercise was to
calculate the additional floor area possible because of adding solar envelopes to the buildings. The area chosen was in South
Park in Downtown Los Angeles. The area is mainly commercial (Figure 31).
35

Figure 31 - The area under study in Downtown Los Angeles.
This neighbourhood was modelled in Revit. Individual buildings were modelled keeping the overall geometry the same as
original, and details were not modelled. The model was thus kept simple, to simplify calculations. For each building, solar
envelopes were generated using the steps described in Section 3.2.2. Solar envelopes were not generating for the surface
parking lots present in the study area. The volume added for each building was then divided into floors. An average floor
height of 4m was considered. Then the total usable floor area of the existing building along with the usable floor area of the
additional floors generated was calculated and compared with the original usable floor area values. Chapters 4 and 5 discuss
the results.
PART II
A solar envelope generation tool was created, using Dynamo, to work with Revit. This script takes in user input to generate
solar envelopes for a given site. Dynamo is a visual scripting tool, used as a plugin with Revit. As mentioned before, there
has been a considerable work done to develop software tools to generate solar envelopes for a given site, but only one
36

developed by Karen Kensek and Alicyn Henkhaus that works with a BIM program
73
. Building information modelling is
becoming increasingly popular within the building industry. Revit is the BIM program that is being increasingly used. Thus,
a tool to generate solar envelopes within Revit can help influence early design decisions more conveniently, without having
to switch programs (Figure 32).
The algorithm for the tool has been derived from the solar envelope generation technique described in section 2.3. The script
takes in spatial and temporal information from the user to generate the required solar envelope geometry. This script only
considers rectangular sites. A possible future work on this tool could be incorporation of other site shapes. The complete
script coding is described in Appendix A.

Figure 32 – A visual overview of the complete script.
3.4. Script algorithm
The script takes in user inputs, which include site width and length, site orientation, shadow fence height, the latitude and the
longitude of the site, the time difference from GMT (without daylight saving), and the beginning of the summer and winter
cut-off times. The reason it takes only the beginning of the cut-off times and not the ends, is because it considers the cut-off
times to be symmetrical about noon, hence only the beginning is required.
Based on these values, the script finds out the coordinates for the four corner points of the site. Using trigonometric
relationships, the coordinates for the summer and the winter ridge points of the envelope are calculated. The last step
involves joining these points to give the solar envelope geometry. Figure 33 describes the algorithm used.

Figure 33 - Script algorithm

73
Kensek, Karen, and Alicyn Henkhaus. 2013. "Solar Access Zoning + Building Information Modeling". Proceedings Of
ASES National Solar Conference.
37

3.4.1. Step 1
For the first step the script takes in spatial and temporal information from the user. Figure 34 shows a screenshot of the input
box. The width (x), the length (y), and the shadow fence height (h) can be in any units as desired by the user, such as in
meters, or feet, or millimetres, or inches, and so on. The script gives an option to choose the output units in the end.

Figure 34 - The user inputs
The latitude and longitude are in degrees. Latitudes to the north of the equator should be entered positive and those to the
south of the equator should be entered as negative. Likewise, longitudes to the east of the prime meridian should be entered
as positive, and those to the west as negative. The grid orientation (θ) is the site rotation from the x axis in degrees (Figure
35). The possible values for this is from 0° to 89°. If the grid orientation is 90°, care should be taken to not enter “90” as
“Grid Orientation”, as the calculation involves finding the tangent of this angle, and tangent of 90 degrees is undefined.
Instead, interchange the inputs for width and length and put Grid Orientation as 0 degree. The output will be the same.
The time difference is the one without considering daylight savings. It is positive for places which are ahead of the GMT and
negative for those which are behind the GMT. The local time (summer) and local time (winter) are the beginning of the
desired cut-off times for summer and winter. Since the script assumes the cut-off times to be symmetrical about noon, only
the starting of the cut-off time is required. This is in hours. Because of the symmetrical nature, only hours till 11am can be
entered. Care should be while putting in the hours. For accurate results, the actual sunrise times should be checked for a
location, and a time after that should be entered.

Figure 35 - The site information.
3.4.2. Step 2
In step 2, the script defines the site boundaries, based on the inputted values for width (x), length (y) and grid orientation (θ).
The script determines the co-ordinates for the four vertices or site edge points, and connects these points to draw the site.

θ
38

Coordinates for point O (refer to Figure 36) – This is the origin, and has co-ordinates (0, 0)

Figure 36 - Calculating co-ordinates for site edge point A
Coordinates for point A (refer to Figure 36)
x- Co-ordinate of point A = OA 1
y- Co-ordinate of point A = AA 1
From the right-angled triangle ∆OAA 1 - OA=x and ∠AOA 1 = θ
Using trigonometric functions,
cos 𝜃 =
𝑂 𝐴 1
𝑂𝐴

𝑂𝐴
1
= 𝑂𝐴 cos 𝜃
𝑶𝑨
𝟏 = 𝒙 𝐜𝐨𝐬 𝜽
sin 𝜃 =
𝐴𝐴
1
𝑂𝐴

𝐴𝐴
1
= 𝑂𝐴 sin 𝜃
𝑨𝑨
𝟏 = 𝒙 𝐬𝐢𝐧 𝜽
∴ Coordinates for point A – (xcosθ, xsinθ)
39

Figure 37 - Calculating co-ordinates for site edge point B
Coordinates for point B (refer to Figure 37)
x- Coordinate of point A = BB 2
y- Coordinate of point A = BB 1
From the right-angled triangle ∆AA 1A 1’, - AA 1= xsinθ and ∠A 1AA 1’ = θ
𝐴𝐴
1
′
cos 𝜃 = 𝐴𝐴
1

𝐴𝐴
1
′
=
𝐴𝐴
1
cos 𝜃
𝐴𝐴
1
′
=
𝑥 sin 𝜃 cos 𝜃
𝐴𝐴
1
′
= 𝑥 tan 𝜃
From the right-angled triangle ∆BB 1A’, - BA 1’= BA+AA 1’ and ∠B 1BA 1’ = θ
Now, BA = y and 𝐴𝐴
1
′
= 𝑥 tan 𝜃
Using trigonometric functions,
𝐵𝐵
1
= 𝐵𝐴
1
′
cos 𝜃
𝐵𝐵
1
= (𝐵𝐴 + 𝐴𝐴
1
′
) cos 𝜃
𝑩𝑩
𝟏 = (𝒚 + 𝒙 𝐭𝐚𝐧 𝜽 ) 𝐜𝐨𝐬 𝜽
From the right-angled triangle ∆CC 2C 2’, - ∠C 2CC 2’ = θ
Now, CO = y, which makes𝐶𝐶
2
= 𝐶𝑂 sin 𝜃 , i.e. 𝐶𝐶
2
= 𝑦 sin 𝜃 ,
Using trigonometric functions,
𝐶𝐶
2
′
cos 𝜃 = 𝐶𝐶
2

𝐶𝐶
2
′
=
𝑦 sin 𝜃 cos 𝜃
40

𝐶𝐶
2
′
= 𝑦 tan 𝜃
From the right-angled triangle ∆BB 2C 2’, - BC 2’= BC-CC 2’ and ∠B 2BC 2’ = θ
𝐵𝐵
2
= 𝐵𝐶
2
′
cos 𝜃
𝐵𝐵
2
= (𝐵𝐶 − 𝐶𝐶
2
′
) cos 𝜃
𝑩𝑩
𝟐 = (𝒙 − 𝒚 𝐭𝐚𝐧 𝜽 ) 𝐜𝐨𝐬 𝜽
∴ Coordinates for point B – [(𝒙 − 𝒚 𝐭𝐚𝐧 𝜽 ) 𝐜𝐨𝐬 𝜽 ,(𝒚 + 𝒙 𝐭𝐚𝐧 𝜽 ) 𝐜𝐨𝐬 𝜽 ]
Coordinates for point C (refer to Figure 38)

Figure 38- Calculating co-ordinates for site edge point C
x- Coordinate of point C = OC 1
y- Coordinate of point C = CC 1
From the right-angled triangle ∆OCC 1, - OC = y and ∠COC 1 = 90° - θ
Using trigonometric functions,
𝑂𝐶
1
= 𝑂𝐶 cos(90° − 𝜃 )
𝑶𝑪
𝟏 = 𝒚 𝐬𝐢𝐧 𝜽 [As cos(90° − 𝜃 ) =sin 𝜃 ]
The x Coordinate would be negative as the point is located in the second quadrant.
𝐶𝐶
1
= 𝑂𝐶 sin(90° − 𝜃 )
𝑪𝑪
𝟏 = 𝒚 𝐜𝐨𝐬 𝜽 [As sin(90° − 𝜃 ) =cos 𝜃 ]
∴ Coordinates for point C – (-ysinθ, ycosθ)
Shadow fence
In case there is a shadow fence, there will be four additional points. These are essentially the same points as the site edge
points, but these have a z component, which is equivalent to the shadow fence height inputted (h). Points D, E, F, G have
same x and y coordinates as points O, A, B and C respectively, plus a z Coordinate equal to the shadow fence h (Figure 39).
41

Figure 39 - Accounting for shadow fence

Figure 40 - Part of the Dynamo script for finding site edge points
3.4.3. Step 3
Step three of the script is finding out the summer and winter ridge points based on given information. It starts with
calculating the solar angles – altitude and azimuth, for summer and winter, at the cut-off time specified. It then uses these
values to find the summer and winter ridge points.
Calculating solar altitude
The solar altitude is calculated using the following formula –
𝑠𝑖𝑛 𝛼 = 𝑐𝑜𝑠 𝐿 𝑐𝑜𝑠 𝛿 𝑐𝑜𝑠 𝐻 + 𝑠𝑖𝑛 𝐿 𝑠𝑖𝑛 𝛿
Where,
α = altitude angle,
L = site latitude, in degrees north or south of the equator,
H = hour angle
δ = declination angle
The site latitude is a user input. Latitudes south of the equator are entered as negative, and those north of the equator as
positive values.
Hour angle is given by the following equation –
Hour angle H = 15° (12 - t)
Where, t = Local Solar Time.
Local solar time is given by,
Point x y z
D 0 0 h
E xcosθ xsinθ h
F (𝑥 − 𝑦 tan 𝜃 ) cos 𝜃 (𝑦 + 𝑥 tan 𝜃 ) cos 𝜃 h
G -ysinθ ycosθ h
42

𝑡 = 𝐿𝑇 +
𝑇𝐶
60

Where,
LT = Local time
TC = Time Correction factor.
The Time Correction Factor TC (in minutes) is given by,
TC = 4(Longitude – LSTM) + EoT
Where,
LSTM = Local Standard Time Meridian
Longitude = site longitude in degrees, positive east of the Prime Meridian and negative west of the Prime Meridian.
EoT = Equation of Time
The Local Standard Time Meridian (LSTM) is defined as,
LSTM = 15°. ∆T GMT
Where ΔT GMT is the difference of the Local Time (LT) from Greenwich Mean Time (GMT) in hours.
The Equation of Time EoT (in minutes) is given by,
𝐸𝑜𝑇 = 9.87 sin(2𝑑 ) − 7.53 cos 𝑑 − 1.5 sin 𝑑
Where 𝑑 =
360
365
(𝑛 − 81) , n is day of the year. For January 1, n = 1, and so on
For summer solstice, n = 172, and thus 𝑑 =
360
365
(172 − 81)
𝑑 = 89.75
Thus,
𝐸𝑜𝑇 = 9.87 sin(2 × 89.75) − 7.53 cos 89.75 − 1.5 sin 89.75
𝑬𝒐𝑻 = −𝟏 . 𝟕𝟔
Plugging in the values into the equation for TC,
TC = 4(Longitude – 15°. ∆T GMT) -1.76
Thus, local solar time,
𝑡 = 𝐿𝑇 +
4(𝐿𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑒 − 15°∆𝑇 𝐺𝑀𝑇 ) − 1.76
60

And hour angle,
H = 15° (12 - 𝐿𝑇 +
4(𝐿𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑒 −15°∆𝑇 𝐺𝑀𝑇 )−1.76
60
)
Declination for summer solstice 𝛿 = 23.45°
Thus solar altitude for summer solstice is given by,
𝑠𝑖𝑛 𝛼 = 𝑐𝑜𝑠 𝐿 𝑐𝑜𝑠 𝛿 𝑐𝑜𝑠 𝐻 + 𝑠𝑖𝑛 𝐿 𝑠𝑖𝑛 𝛿
𝛼 = sin
−1
(𝑐𝑜𝑠 𝐿 𝑐𝑜𝑠 𝛿 𝑐𝑜𝑠 𝐻 + 𝑠𝑖𝑛 𝐿 𝑠𝑖𝑛 𝛿 )
𝛼 = sin
−1
(cos 𝐿 cos 23.45° cos [12 − 𝐿𝑇 +
4(𝐿𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑒 − 15°∆𝑇 𝐺𝑀𝑇 ) − 1.76
60
] + sin 𝐿 sin 23.45°)
43

𝜶 = 𝐬𝐢𝐧
−𝟏 (cos 𝑳 ×0.92× cos [𝟏𝟐 − 𝑳𝑻 +
𝟒 (𝑳𝒐𝒏𝒈𝒊𝒕𝒖𝒅𝒆 − 𝟏𝟓 °∆𝑻 𝑮𝑴𝑻
) − 𝟏 . 𝟕𝟔
𝟔𝟎
] + sin 𝑳 ×0.4)

Figure 41 - Part of the Dynamo script for finding solar altitude for summer
For winter solstice, n = 355, and thus 𝑑 =
360
365
(355 − 81)
𝑑 = 270.24
Thus,
𝐸𝑜𝑇 = 9.87 sin(2 × 270.24) − 7.53 cos 270.24 − 1.5 sin 270.24
𝑬𝒐𝑻 = 𝟏 . 𝟕𝟔
Plugging in the values into the equation for TC,
TC = 4(Longitude – 15°. ∆T GMT) +1.76
Thus, local solar time,
𝑡 = 𝐿𝑇 +
4(𝐿𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑒 − 15°∆𝑇 𝐺𝑀𝑇 ) + 1.76
60

And hour angle,
H = 15° (12 - 𝐿𝑇 +
4(𝐿𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑒 −15°∆𝑇 𝐺𝑀𝑇 )+1.76
60
)
Declination for winter solstice 𝛿 = −23.45°
Thus solar altitude for winter solstice is given by,
𝑠𝑖𝑛 𝛼 = 𝑐𝑜𝑠 𝐿 𝑐𝑜𝑠 𝛿 𝑐𝑜𝑠 𝐻 + 𝑠𝑖𝑛 𝐿 𝑠𝑖𝑛 𝛿
𝛼 = sin
−1
(𝑐𝑜𝑠 𝐿 𝑐𝑜𝑠 𝛿 𝑐𝑜𝑠 𝐻 + 𝑠𝑖𝑛 𝐿 𝑠𝑖𝑛 𝛿 )
𝛼 = sin
−1
(cos 𝐿 cos (-23.45°) cos [12 − 𝐿𝑇 +
4(𝐿𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑒 − 15°∆𝑇 𝐺𝑀𝑇 ) + 1.76
60
] + sin 𝐿 sin (-23.45°))
𝜶 = 𝐬𝐢𝐧
−𝟏 (cos 𝑳 ×0.92× cos [𝟏𝟐 − 𝑳𝑻 +
𝟒 (𝑳𝒐𝒏𝒈𝒊𝒕𝒖𝒅𝒆 − 𝟏𝟓 °∆𝑻 𝑮𝑴𝑻
) + 𝟏 . 𝟕𝟔
𝟔𝟎
] − sin 𝑳 ×0.4)
44

Figure 42 - Part of the Dynamo script for finding solar altitude for winter
Calculating solar azimuth
The solar azimuth is calculated using,
cos 𝜑 =
sin 𝛿 − sin 𝛼 sin 𝐿 𝑐𝑜𝑠 𝛼 . cos 𝐿
Where:
α = altitude angle,
φ = azimuth angle,
L = site latitude, in degrees north or south of the equator,
δ = declination angle
The script takes in the solar altitude value from the previous portion, and the latitude is given as user input.
Declination for summer solstice 𝛿 = 23.45°
Thus, the summer solar azimuth is given by,
𝜑 = cos
−1
[
sin 23.45° − sin 𝛼 sin 𝐿 𝑐𝑜𝑠 𝛼 . cos 𝐿 ]
𝝋 = 𝐜𝐨𝐬 −𝟏 [
𝟎 . 𝟒 − 𝐬𝐢𝐧 𝜶 𝐬𝐢𝐧 𝑳 𝒄𝒐𝒔 𝜶 . 𝐜𝐨𝐬 𝑳 ]

Figure 43 - Part of the Dynamo script for finding solar azimuth for summer
45

Declination for winter solstice 𝛿 = −23.45°
Thus, the winter solar azimuth is given by,
𝜑 = cos
−1
[
sin(−23.45°) − sin 𝛼 sin 𝐿 𝑐𝑜𝑠 𝛼 . cos 𝐿 ]
𝝋 = 𝐜𝐨𝐬 −𝟏 [
(−𝟎 . 𝟒 ) − 𝐬𝐢𝐧 𝜶 𝐬𝐢𝐧 𝑳 𝒄𝒐𝒔 𝜶 . 𝐜𝐨𝐬 𝑳 ]

Figure 44 - Part of the Dynamo script for finding solar azimuth for winter
Summer ridge point
The site in 3D, with a street grid of θ degrees, a width of x units, and a length of y units is calculated (Figure 45). These
values are all obtained from user inputs. The determination of co-ordinates for points A, B, and C has been described in the
previous section (3.5.2). S is the summer envelope ridge point, and S 1, S 2 and S 3 are its x, y, and z projections. Based on the
user inputs, the script calculates the co-ordinates for the point S. The top edges of the red triangles represent the morning
solar rays that pass over the site to intersect a predetermined boundary. The complete solar envelope is also shown in the
underlying plan view.

Figure 45 - Calculating coordinates for summer ridge point
Calculating coordinates for summer ridge point S –
46

This is a description of how the script calculates the co-ordinates for S.
X- Coordinate
From figure, the x-coordinate S x is equal to OS 1.
Using properties of similar triangles,
𝑆 𝑥 csc 𝜑 𝑥 cos 𝜃 =
𝑥 csc(𝜑 + 𝜎 )
2𝑥 cos 𝜃
𝑺 𝒙 =
𝒙 𝐬𝐢𝐧 𝝋 𝟐 𝐬𝐢𝐧 (𝝋 + 𝜽 )

Figure 46 - Part of the Dynamo script for finding x Coordinate for summer ridge point
Y- Coordinate
From figure, the y-coordinate S y is equal to OS 2.
Using properties of similar triangles,
𝑦 − 𝑆 𝑦 = 𝑦 ×
𝑆 𝑥 cos 𝜑 𝑦 sin(𝜑 + 𝜃 )

𝑺 𝒚 = 𝒚 −
𝒙 𝐜𝐨𝐬 𝝋 𝐬𝐢𝐧 𝝋 𝟐 𝒔𝒊𝒏 𝟐 (𝝋 + 𝜽 )

Figure 47 - Part of the Dynamo script for finding y Coordinate for summer ridge point
Z- Coordinate
From figure, the z-coordinate S z is equal to SS 3.
In ∆ OB 1B 2,
47

ℎ = 𝑥 sec[90° − (𝜑 − 𝜃 )] tan 𝛼
ℎ = 𝑥 csc(𝜑 + 𝜃 ) tan 𝛼
ℎ =
𝑥 tan 𝛼 sin(𝜑 + 𝜃 )

Using similar triangles for ∆ OB 1B 2 and ∆ OSS 3,
𝑆 𝑧 =
𝑏 × ℎ
𝑎
𝑆 𝑧 =
𝑆 𝑥 csc 𝜑 𝑥 sec[90° − (𝜑 + 𝜃 )]
×
𝑥 tan 𝛼 sin(𝜑 + 𝜃 )

𝑺 𝒛 =
𝒙 𝐭𝐚𝐧 𝜶 𝟐𝐬𝐢𝐧 (𝝋 + 𝜽 )

Figure 48 - Part of the Dynamo script for finding z Coordinate for summer ridge point
Winter ridge point
The co-ordinates for the winter ridge point can be calculated using the same equations as for summer ridge point. Only in this
case the values of solar altitude ( α) and azimuth (φ) would be different. The script uses the same equations, but takes in the
winter solar altitude and azimuth values instead.
𝑾 𝒙 =
𝒙 𝐬𝐢𝐧 𝝋 𝟐 𝐬𝐢𝐧 (𝝋 + 𝜽 )

Figure 49 - Part of the Dynamo script for finding x Coordinate for winter ridge point
𝑾 𝒚 = 𝒚 −
𝒙 𝐜𝐨𝐬 𝝋 𝐬𝐢𝐧 𝝋 𝟐 𝒔𝒊𝒏 𝟐 (𝝋 + 𝜽 )

48

Figure 50 - Part of the Dynamo script for finding y Coordinate for winter ridge point
𝑾 𝒛 =
𝒙 𝐭𝐚𝐧 𝜶 𝟐𝐬𝐢𝐧 (𝝋 + 𝜽 )

Figure 51 - Part of the Dynamo script for finding z Coordinate for winter ridge point
Height of the envelope
The height of the final envelope is based on the z-coordinates of the summer and winter ridge points. Whichever is less will
be the final envelope height. After calculating the co-ordinates, the script compares the values of the z-coordinates and
whichever is smallest is used as the value for z-coordinate for both summer and winter ridge points (Figure 52).

Figure 52 - Comparing Z-coordinate values
The script then moves to step four to generate the final envelope.
49

3.4.4. Step 4
In the final step, all the points generated in the previous sections are joined to create the final envelope. Based on input, there
are four possible ways to generate the output. If the grid orientation is zero, the envelope shape is different than when grid
orientation is not zero. The same points are still valid in both case, the way of joining these points is different (Figure 53).
In case grid orientation is zero degrees, the surfaces created are – OAS, ASWB, BWC, and CWSO. In case the grid
orientation is not zero degrees, the surfaces created are – OWSA, ASB, BSWC, and CWO.

Figure 53 - Envelope shape when grid orientation is zero v. when it is not zero. S and W are the summer and winter ridge
points. Changing the grid orientation moves these points and changes the order of joining them.

Figure 54 - Part of the Dynamo script where the code determines which of the four possible outputs to follow.
In case of a shadow fence, there are four additional points, hence four additional surfaces generated (Figure 56). The final
output is a .sat file, which can be transferred to many 3D modelling programs. The script has also been connected to Revit,
such that upon running the program, the envelope geometry automatically imports into Revit as a conceptual mass. While
generating the output, the user can select the desired output units (Figure 58). To create the .sat file, the user has to input the
file path (where the file is to be saved) and the file name.

Figure 55 – Joining of the vertices when grid orientation is a) zero, b) not zero.
50

Figure 56 - Joining points for shadow fence

Figure 57 - The five possible outputs

Figure 58 – The .sat output box. Users have a choice of output units

Figure 59 - Import to Revit
51

3.5. Chapter summary
A Dynamo script was created to work with Revit to generate solar envelopes. Next, solar envelope generation principles for
sites with existing buildings were developed. There are three ways to add more volume to an existing building without
casting additional shadows – on the building site, on the building sides, and on the building roof. Five different building
geometries were considered, and solar envelopes for the site plus the building was generated. Five different latitudes and
three different cut-off times were considered for each test case and the percentage of additional volume possible were
calculated and compared.
Possible urban applications were then tested out on a neighbourhood in downtown Los Angeles. Solar envelopes for each
building were generated, and the additional floor area possible was calculated in terms of total usable floor area, and
compared with the existing usable floor area.

52

CHAPTER 4
4. RESULTS
From the previous chapter, there were three stages of the investigation. The first stage was creating a solar envelope
generating tool. This was created in Dynamo, to work with Revit. This script takes in user input to generate solar envelopes
for a given site. Dynamo is a visual scripting tool, used as a plugin with Revit. The inputs include site width and length, site
orientation, shadow fence height, the latitude and the longitude of the site, the time difference from GMT (without daylight
saving), and the beginning of the summer and winter cut-off times. The reason it takes only the beginning of the cut-off times
and not the ends, is because it considers the cut-off times to be symmetrical about noon, hence only the beginning is required.
The script algorithm is explained in Section 3.4. The script was tested for a number of times, before proceeding on to the next
stage.
In the second stage, solar envelope principles were researched and developed. There are three locations on a site with a
building solar envelopes can be generated for. Volume can be added to the building site, within the site’s solar envelope.
Volume can be added to the building roof, considering the roof as a site, within its solar envelope. Volume can be added to
the building side that is always in shadow within the cut-off times.
Factors affecting solar envelope geometry were studied. Two factors were considered and tested – the site latitude and the
envelope cut-off times. Two building geometries were tested. The building site is rectangular and is the same for all test
cases. The first building geometry considered is a rectangular building. This building sits within the site. Five locations with
different latitudes were considered and envelopes generated. Next, for each latitude, three different cut-off times were tested.
The next geometry considered was an L-shaped building, which sits on the same site as before, and has the same building
height. Four test geometries for the L-shaped building were considered. The same parameters for latitude as before were
considered and tested. All four geometries were tested for five different latitudes, but the same cut-off time. The volumes of
the resulting envelopes were calculated and compared (Figure 60).

Figure 60 - Test case examples
The third stage investigated the feasibility of the principle, by testing out the principles on a neighbourhood in downtown Los
Angeles. The neighbourhood was modelled in Revit. The solar envelopes for each building was generated in the way
described in Section 3.2. The envelope volume was then divided into floors of 4m and the usable floor area possible was
calculated. The usable floor area in this case is defined as the portions of the floor plate that has a clear floor to floor height of
4m.any portion of the floor plate that has a height less that 4m have not been considered while calculating the usable floor
area.
There are two sets of results: the results from the test cases, and the results from the urban application of the concept. The
urban application of the concept calculates the original usable floor area of each building and the new total usable floor area
of each building located within the area of study. The test cases include a calculation of the original volume, the envelope
volume, and the percentage change in volumes.
4.1. Test for volume vs. latitude and cut-off times
53

The volume added was calculated as a percentage of the original building volume. Latitude and cut-off times were tested
simultaneously for the rectangular geometry. For the L-shaped geometries only one cut-off time was tested and five different
latitudes. Tables 1 and 2 sum up the values for all the five geometries tested.
Table 1 - Percentage of volume added for rectangular geometry.
Rectangular Geometry
Cut-off times - 7am to 5pm (summer), 9am to 3pm (winter)
Latitude Percentage of volume
added to site
Percentage of volume
added to roof
Percentage of volume
added to building
Total percentage of volume
added
10.5 30 8 8.5 46.5
22.5 26 7 7.8 40.8
34.05 19 6 0 25
48.2 14 4 0 18
51.5 10 2 0 12
Cut-off times - 8am to 4pm (summer), 9am to 3pm (winter)
Latitude Percentage of volume
added to site
Percentage of volume
added to roof
Percentage of volume
added to building
Total percentage of volume
added
10.5 48 16 8.3 72.3
22.5 41 12 7.6 60.6
34.05 33 9 0 42
48.2 16 4 2 22
51.5 11 3 3 17
Cut-off times - 7am to 5pm (summer), 8am to 4pm (winter)
Latitude Percentage of volume
added to site
Percentage of volume
added to roof
Percentage of volume
added to building
Total percentage of volume
added
10.5 29 6 8.3 43.3
22.5 24 5 7.7 36.7
34.05 19 4 0 23
48.2 14 3 0 17
51.5 0* 0* 0* 0*
*The sun rises and sets within the winter cut-off times for this location, hence no volume could be added.
Table 2 - Percentage of volume added for L-shaped geometries.
Cut-off times - 7am to 5pm (summer), 9am to 3pm (winter)
1. L Geometry (└)
Latitude Percentage of volume
added to site
Percentage of volume
added to roof
Percentage of volume
added to building
Total percentage of volume
added
10.5 39 8.2 9.2 56.4
22.5 34 7.1 7.9 49
34.05 25 6.3 0 31.3
48.2 18 5 0 23
51.5 12 3 0 15
2. L Geometry (┘)
54

Latitude Percentage of volume
added to site
Percentage of volume
added to roof
Percentage of volume
added to building
Total percentage of volume
added
10.5 39 9 9.1 57.1
22.5 34 7.5 7.6 49.1
34.05 25 6.8 0 31.8
48.2 18 4.7 0 22.7
51.5 12 2.5 0 14.5
3. L Geometry (┐)
Latitude Percentage of volume
added to site
Percentage of volume
added to roof
Percentage of volume
added to building
Total percentage of volume
added
10.5 39 8.5 9.3 56.8
22.5 34 6.8 7.3 48.1
34.05 25 5.9 0 30.9
48.2 18 4.2 0 22.2
51.5 12 2.6 0 14.6
4. L Geometry (┌)
Latitude Percentage of volume
added to site
Percentage of volume
added to roof
Percentage of volume
added to building
Total percentage of volume
added
10.5 39 8.8 9.4 57.2
22.5 34 7.4 7.6 49
34.05 25 5.6 0 30.6
48.2 18 4.2 0 22.2
51.5 12 2.9 0 14.9

4.2. Urban application results

Los Angeles (34.05°N latitude) was chosen as the location for the urban study. A neighbourhood in downtown Los Angeles
was selected, and envelopes were generated for each building. The volume added was divided into floors of height 4m. The
new total usable floor area of each building, including the new useful floor area added was calculated and compared with the
original usable floor areas of each building (Table 3). The site plan of the neighbourhood shows that each building has been
assigned a number for cross-reference (Figure 61).

55

Figure 61 - Key plan for buildings.
4.2.1. Example calculation of increase in usable floor area
The usable floor area in this case is defined as the portions of the floor plate that has a clear floor to floor height of 4m.any
portion of the floor plate that has a height less that 4m have not been considered while calculating the usable floor area
(Figure 62).
Considering building number 45 (Figure 62) -
1. Number of floors = 8
2. Floor area of each floor = 1371 m
2

3. Site area = 1645 m
2

4. Total usable floor area without envelope = 1371𝑚 2
× 8 = 10968𝑚 2

5. Number of floors added = 4
6. Floor area of each floor added (usable) –
a. Level 9 – 1071
b. Level 10 – 949
c. Level 11 – 590
d. Level 12 – 307
7. Total usable floor area with additional floors = (10968 + 1071 + 949 + 590 + 307)𝑚 2
= 12995𝑚 2

56

Figure 62 - Addition and calculation of new floors and floor areas.
57

Table 3 - Increase in usable floor area
Building Number
of floors
Usable
floor
area
(m
2
)
Volume
added
to site
Volume
added
to sides
Volume
added to
roof
Number of
additional
floors
possible
New usable
floor area
possible
(m2)
Remarks
Bldg 1 5 59815 No No Yes 10 81855.0 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof. Because of
large roof area, a large solar
envelope is possible.
Bldg 2 11 45584 No No Yes 5 56604.0 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 3 2 7590 Yes No No 9 39780.0 Site envelope larger than actual
building volume. New floor area
calculated considering only the
site envelope. This envelope can
have 9 floors possible.
Bldg 4 11 21703 No No Yes 3 24895.0 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 5 4 2272 No No Yes 3 5944.0 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 6 1 457 No No Yes 2 870.6 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 7 2 5084 No No Yes 4 9820.0 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 8 1 1457 No No Yes 3 4010.0 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 9 3 1839 No No Yes 3 3060.0 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 10 1 719 No No Yes 3 1940.0 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 11 1 1441 No No Yes 3 3718.0 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 12 31 62465 No No Yes 4 66493.0 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 13 1 972 No No Yes 2 2222.0 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
58

Bldg 14 6 21894 Yes No No 9 31212.0 Site envelope larger than actual
building volume. New floor area
calculated considering only the
site envelope. This envelope can
have 9 floors possible.
Bldg 15 3 3369 Yes No No 5 8800.0 Site envelope larger than actual
building volume. New floor area
calculated considering only the
site envelope. This envelope can
have 9 floors possible.
Bldg 16 7 12943 No No Yes 4 16023.0 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 17 1 1393 No No Yes 4 3793.0 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 18 2 2186 No No Yes 3 3986.0 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 19 2 2046 No No Yes 3 3846.0 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 20 4 5948 Yes No No 4 6160.0 Site envelope larger than actual
building volume. New floor area
calculated considering only the
site envelope. This envelope can
have 9 floors possible.
Bldg 21 23 54211 Yes No Yes 5 70883.2 Because of building height,
addition to both site and roof
possible. The roof envelope can
have 5 possible floors. The site
envelope, in itself can have 9
possible floors
Bldg 22 14 42868 No No Yes 4 47392.0 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 23 5 7025 No No Yes 3 9665.0 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 24 1 1585 No No Yes 4 5585.0 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 25 1 767 No No Yes 4 2727.0 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 26 1 1070 No No Yes 4 3618.0 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 27 4 6708 No No Yes 4 10236.0 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
59

Bldg 28 2 3004 No No Yes 3 5854.0 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 29 2 1870 No No Yes 4 4270.0 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 30 2 1870 No No Yes 4 4270.0 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 31 3 2805 No No Yes 4 5205.0 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 32 20 42920 Yes No Yes 5 57204.0 Because of building height,
addition to both site and roof
possible. The roof envelope can
have 5 possible floors. The site
envelope, in itself can have 8
possible floors
Bldg 33 5 17070 Yes No No 8 24272.0 Site envelope larger than actual
building volume. New floor area
calculated considering only the
site envelope. This envelope can
have 9 floors possible.
Bldg 34 2 928 No No Yes 2 2128.0 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 35 2 1758 No No Yes 3 3445.5 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 36 2 1758 No No Yes 3 3445.5 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 37 1 879 No No Yes 3 2566.5 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 38 1 879 No No Yes 3 2566.5 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 39 1 879 No No Yes 3 2566.5 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 40 3 2364 No No Yes 3 3826.5 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 41 1 788 No No Yes 3 2250.5 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 42 1 788 No No Yes 3 2250.5 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
60

Bldg 43 2 1576 No No Yes 3 3038.5 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 44 2 1576 No No Yes 3 3038.5 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 45 8 10968 No No Yes 4 12995.5 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 46 4 12380 No No Yes 5 18980.0 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof
Bldg 47 3 5988 No No Yes 3 9057.0 Building covers most of the site
(>80% of site area). Hence, site
envelope not possible. Volume
only added to roof

4.3. Chapter summary
Solar envelopes for each test case were generated and data collected in terms of the percentage of the original volume added
to each test case. For the urban application study, solar envelopes were generated and the results were expressed as the
change in floor area ratios. The usable floor area of each building were calculated. After the solar envelope was developed,
the envelope volume was divided into additional floors possible, and the total usable floor area of the building including the
new floors added was calculated. Chapter 5 analyses the results of the tests.

61

CHAPTER 5
5. ANALYSIS
The data presented in Chapter 4 for the test cases was analysed in terms of the relationship between the envelope volume and
the location of the site as well as the cut-off times. For the urban application study, where the location and the cut-off times
were fixed prior to the study, the change in building usable floor area due to the new solar envelope volume added was
analysed.

5.1. Site location vs. volume added
Results indicate that the latitude of the site is directly related to the amount of volume that could possibly be added. The
latitude value is inversely related to the volume added. This means that the further from the equator, the less total volume that
is added.
This relates to factors affecting solar envelope volume, one of which being the latitude, as discussed in Section 2.4.4. For the
same site, varying the latitude will change the envelope height. Keeping the cut-off times and the site dimensions the same,
sites at latitudes closer to the equator will have larger height and volume, and those away from the equator will have smaller
heights and volumes, because the sun is usually at a higher angle as one moves closer to the equator, and lower when one
moves away from the equator. The solar envelope geometry being based off the sun angles thus vary accordingly (Figure 63).

Figure 63 - Latitude versus site and roof envelope heights for the same rectangular building.
Thus, the volume being added to the building site, considering the site to be empty, relates to this. This means that the
percentage of volume that is possible to be added to the same building site will be more if it is located closer to the equator,
than if it is located further away, at higher latitudes (Figure 63).
The volume that is being added to the roof also relates to the discussion in Section 2.4.4. The way to add volume to roof is
discussed in Section 3.2.2. If the roof is considered as a site, and using the roof dimensions as site dimensions, and the same
specified cut-off times as before, a solar envelope is generated and placed on the roof, anything built within this volume will
not cast any additional shadows. This can also be thought of as a site with the same dimensions as the building roof, and a
shadow fence the same as the height of the building. Thus, the volume added to the roof is related to the latitude in the same
way as that added to the building site. Buildings sites located closer to the equator will have larger volumes added to the roof
than sites located away from the equator (Figure 63).
The amount of volume that could be added to the building sides is more dependent on the cut-off times, than on the latitude.
This volume is dependent on the sun’s path for the particular location and the selected cut-off times. Since, the sun path
varies based on the latitude of the place, so latitude does affect the amount of volume added. However, this relationship is not
linear, unlike that of the volume added to the site and the roof. If within the cut-off times, the building casts shadows, such
that sides of the building is always under shadow, new volumes could be added on to those sides. Based on the results, and
observing the sun paths of the different locations, it was seen that sites located below the 23.5° latitude will always have
buildings which cast shadow on one side of the building. Thus, the test buildings in these locations (10.5°N and 22.5°N) have
10.5°N 51.5°N
62

solar envelope volumes for the sides always under shadow. This is independent of cut-off times chosen (Figure 66, Figure
67).
Moving away from the 23.5° latitude, it was seen that the sun paths become such that the test buildings cast shadows on more
than one side. For these cases, the building side envelope added is directly related to the cut-off times (Figure 66, Figure 67).
The graphs below show the relationships between solar envelope volumes added and the latitude and cut-off times. The first
set of graphs are for the rectangular geometry (Figure 64), and the next set of graphs are for the L-shaped geometry (Figure
65).

Figure 64 - Latitude and cut-off times v. Envelope volume - Rectangular geometry.
0
10
20
30
40
50
60
70
80
0 10 20 30 40 50 60
Percentage of volume added
Latitude v. Envelope volume
(7am-5pm summer, 9am-3pm
winter)
0
10
20
30
40
50
60
70
80
0 10 20 30 40 50 60
Percentage of volume added
Latitude v. Envelope volume
(8am-4pm summer, 9am-3pm
winter)
0
10
20
30
40
50
60
70
80
0 10 20 30 40 50 60
Percentage of volume added
Latitude v. Envelope volume
(7am-5pm summer, 8am-4pm
winter)
63

Figure 65 - Latitude v. Envelope volume added - L-geometry, 4 orientations. The cut-off time has been kept the same in all 4
cases (summer 7am-5pm, winter 9am-3pm)
Regardless of the cut-off times used, there is an indirectly proportional and almost linear relationship between the volumes
added to the site and the roof and the site latitude. While the actual values being added will differ from case to case, the basic
trend remains the same.
5.2. Cut-off times vs. volume added
The cut-off times also affected the amount of volume being added. As discussed in Section 2.4.5, the earlier the cut-off times
begin in the morning, and the later they go into the afternoon, the smaller the envelope height, and volume is. This is because
the sun angles are much lower in the early morning and late afternoon, and much steeper near midday, at all seasons
throughout the year. Therefore, the longer the period of solar access required the smaller the volume of the envelope
constructed.
0
10
20
30
40
50
60
0 10 20 30 40 50 60
Percentage of volume added
Latitude v. Envelope volume
L Geometry (└)
0
10
20
30
40
50
60
0 10 20 30 40 50 60
Percentage of volume added
Latitude v. Envelope volume
L Geometry (┘)
0
10
20
30
40
50
60
0 10 20 30 40 50 60
Percentage of volume added
Latitude v. Envelope volume
L Geometry (┐)
0
10
20
30
40
50
60
0 10 20 30 40 50 60
Percentage of volume added
Latitude v. Envelope volume
L Geometry (┌)
64

The volume that is being added to the site follows this. As can be seen from the graphs, less volume gets added when the cut-
off times are longer, and more is added for shorter cut-off times. This is the same with the volume that is being added to the
building roof.
The volume that is being added to the sides is more sensitive to the cut-off times. This is especially true for all sites located
above the 23.5° latitudes. As explained in Section 3.2.2 for sites located below 23.5° latitudes, it was possible to add solar
envelopes to the sides, regardless of the cut-off times chosen. This is because, for these latitudes, the sun moves in such a
way that the building always casts shadows on one side, throughout the cut-off times. But for those sites, located above the
23.5°, the cut-off times determine if a solar envelope for the building side can be generated. If within the cut-off times, the
building casts shadows only on one side of the building (regardless of which side), only then can extra volume be added to
the side that is always under shadows, without casting additional shadows (Figure 66).

Figure 66 - Effect of cut-off times on the addition of building side envelope for different latitudes below and above 23.5°N for
the same cut-off times. For the same building, a side envelope can always be added if located below 23.5°N, but for locations
above 23.5°N the addition of a side envelope is dependent on the cut-off times chosen.
65

In this case, for the site located at 34.05°N latitude, within the chosen cut-off times, the building casts shadows on both sides.
Hence, creating a solar envelope for the building sides it not possible in this case. The effect of cut-off times is more
prominent for the 48.2°N and 51.5°N latitudes. In both cases, when the summer cut-off times were chosen as 7am to 5 pm, no
solar envelope for the sides could be generated. This is because within these times, the sun moves in such a way that the
building does not cast shadows on only one side. However, when the cut-off times were chosen as 8 am to 4 pm in the
summer (a shorter period of solar access), it was possible to generate solar envelopes for the building sides. This is because,
within these cut off times, the sun has moved such that now the building casts shadows on only one side. Hence, solar
envelopes for each side under shadow could be generated (Figure 67).

Figure 67 - Effect of cut-off times on the building side envelope added for sites located 23.5°N and up. For the same location
varying the cut-off times can result in volume being added to the building side or not.
5.3. Urban application
Individual envelopes were generated for each building in downtown Los Angeles (34.05°N latitude). The cut-off times were
chosen as 7am to 5pm in summer and 9am to 3pm in winter. The volume added was divided into floors, 4m in height, and the
new total usable floor area of the building including the new floors added was calculated.
As seen from the test cases in the previous section, no building side envelope volume could be added for buildings located at
34.05°N latitude (which is the latitude for Los Angeles), for cut-off times 7am to 5pm in summer and 9am to 3pm in winter.
66

For every building tested within the area of study, volumes could only be added to the building site and the roof, and not on
the sides. Two scenarios were observed. For most buildings, the building footprint occupies most of the site (> 80%). For
these cases, the site envelope could not be added. Only the roof envelope could be added.
The second scenario involved sites and buildings where the building footprint did not occupy most of the site area. For these
cases a site envelope could be generated. Whether or not a roof envelope could be generated depended on the actual building
height and the site area. For large site areas, and smaller building heights, the site envelope generated was such that the height
of it was larger than the building height. Thus, the envelope completely “engulfs” the building. This implies that had a solar
envelope been considered for the site prior to building construction, a larger usable floor area would have been possible. In
other cases, it was seen that the building height was larger than the height of the site envelope generated. For such cases, a
roof envelope could be added as well. These buildings had the most addition of usable floor area.
In all cases, it was noted that more floors could be added if the surface on which the envelope is being generated (either the
roof or the site or both) has more surface area. This is in compliance with the discussion in Section 2.4.1 about how larger
site dimensions mean more envelope volume and height. More envelope height implies more number of floors possible.
Thus, buildings where volume could only be added to the roof, it was seen that those with smaller roof area had fewer floors
added and those with a larger roof area had more number of floors added. Similarly, for the buildings where a site envelope
could be generated, a larger site area means an envelope with more height. Here the existing building height plays a crucial
role. If the existing building height is more than the site envelope height, then the roof envelope could be added too. Again,
the roof envelope height depends on the roof area. The larger the area, the more the envelope height, and more floors
possible.
The graph below (Figure 68) shows a comparison between the original usable floor area values and the new usable floor area
values for each building. Figure 69 shows the results.

Figure 68 - Comparison between original and new usable floor area values
0
5000
10000
15000
20000
25000
30000
35000
40000
45000
50000
55000
60000
65000
70000
75000
80000
Bldg 1
Bldg 2
Bldg 3
Bldg 4
Bldg 5
Bldg 6
Bldg 7
Bldg 8
Bldg 9
Bldg 10
Bldg 11
Bldg 12
Bldg 13
Bldg 14
Bldg 15
Bldg 16
Bldg 17
Bldg 18
Bldg 19
Bldg 20
Bldg 21
Bldg 22
Bldg 23
Bldg 24
Bldg 25
Bldg 26
Bldg 27
Bldg 28
Bldg 29
Bldg 30
Bldg 31
Bldg 32
Bldg 33
Bldg 34
Bldg 35
Bldg 36
Bldg 37
Bldg 38
Bldg 39
Bldg 40
Bldg 41
Bldg 42
Bldg 43
Bldg 44
Bldg 45
Bldg 46
Bldg 47
Original v New usable floor area (m2)
Total usable floor area (m2) New usable floor area possible (m2)
67

Figure 69 - Urban application results. The existing building geometries are in purple. The new envelopes added are in white.
5.4. Chapter summary
Results support the hypothesis that it is possible to create solar envelopes for sites with existing buildings, using same
principles as those used to generate for empty sites. The size of this solar envelope is affected by the site location (in terms
of latitude) and the cut-off times chosen for solar access. There is a linear relationship between the location of the site and the
cut-off times with the amount of volume that can be added.
When the principles were applied on an urban neighbourhood, two scenarios were observed. In the first, when the building
occupied almost all of the site, an envelope could be added only to the roof of the building. In the second, where the building
footprint occupies less that 50% of site area, a site envelope was possible. If the building height was greater than the site
envelope height, an additional roof envelope was also possible for such buildings.
68

CHAPTER 6
6. CONCLUSIONS
Solar envelopes for sites with existing buildings were studied. A digital tool was developed in Dynamo to work with Revit
for generating solar envelopes. This tool takes user inputs, which include site width and length, site orientation, shadow fence
height, the latitude and the longitude of the site, the time difference from GMT (without daylight saving), and the beginning
of the summer and winter cut-off times. Only cut-off times symmetrical about noon can be read by the tool. Non-rectangular
sites, sloped sites, non-symmetric cut-off times, and non-equal shadow fences were not included in the scope of this tool.

It is possible to added volume to an existing building without casting extra shadows. There are three possible places. Volume
can be added to the building site, within the site’s solar envelope. Volume can be added to the building roof, considering the
roof as a site, within its solar envelope. Volume can be added to the building side that is always in shadow within the cut-off
times. The amount of volume added is case-specific and it is dependent on the existing building geometry and site
dimensions. Given the same site dimensions and building geometry, more volume can be added if the site is located closer to
the equator, for the same cut-off times. Smaller cut-off times also mean more volume being added, and for sites with latitudes
23.5° and up this implies a possible addition of the side envelope, as for these latitudes the side envelope is entirely
dependent on the cut-off times.
6.1. Applications
This information can be part of zoning ordinances, by controlling additions to existing buildings, not built within a solar
envelope. This would ensure additions do not cast additional shadows. Building retrofitting works could also use this
information. Additions and retrofits can be safely made without casting more shadow, if kept within the solar envelope
boundaries. If the volume added is large enough, extra floors can be added to existing buildings. This would increase rentable
space of the building.
If addition of new floors is not a feasible option (see Section 6.2 for points to be considered while deciding feasibility of new
floors), there could be other uses of the solar envelope volume. The roof volume could be used to place building systems,
such as PV arrays, or additional roof top HVAC units if required. If the roof envelope height is large enough, and the
additional floors have a large enough area such that their construction is justified, this strategy could be used to add both
floors as well as the supporting building systems required such as HVAC unit for those floors, all within the roof envelope.
This geometry could also guide the design of outdoor usable spaces such as roof gardens and other rooftop open areas. Again,
if the roof envelope height is big enough, a combination of floors and open spaces and landscaped areas can be constructed
on the roof Figure 70).
The building side envelope volume can be used to put up solar shading devices, such as overhangs and fins. PV panels could
also be integrated along with the shading devices onto the building sides. If solar shading devices are not required, and the
envelope is deep enough, balconies could be added within the envelope volume, if the building design supports it (Figure 70).
The site envelope volume could also be used as a development guide on the site. If there are plans to construct additional
buildings on the site, the solar envelope could constraint the volume of development to ensure solar access. This strategy is
especially useful for projects that have planned for future expansions. This envelope geometry can also be used to inform
landscaping decisions, such as constraining heights of trees within the envelope height. Other open air spaces such as
pavilions and amphitheatres could also be designed to be within the envelope volume for continued solar access of the
surrounding buildings (Figure 70).
69

Figure 70 - Possibilities. This is an illustration showing what the solar envelope volume generated can be used for. On the
left is the original building. On the right are the possible uses. This shows the ideal scenario where the site and the building
can have all the three envelope volumes added.
6.2. Urban application constraints
However, the feasibility of such application will change based on the scenario. For example, for a building with a small
footprint, which occupies all of its site, it is theoretically possible to add an envelope to the roof (as seen in the urban
application study). However, because of the small footprint, the envelope generated would also be small, with not many
floors being added. It is to be remembered that the floors that are being added will have a lesser floor area that the existing
building floor areas. For such a scenario, the construction cost per square foot will determine the feasibility of adding the
floors. It might be so that the cost does not justify the addition, and thus the principle cannot be applied to such a building.
For other buildings which are larger in volume and floor area envelopes with more height are possible. This means that more
number of floors could be added. In such a case, the cost may be justified, as such additions would lead to more useful
rentable space. However, for these cases, the actual design of the building will determine if such an addition is possible.
To add floors would mean extending the building service cores to the additional floors. This includes staircases and elevators.
It would need to be determined if because of the new floors additional egress routes are required. If that is the case then more
staircases would need to be added, which will add on to the construction costs, and the building structure.
Building systems loads will change, and the existing HVAC systems will need to be upgraded to cater to the new floors. It
may be so that additional service floors are required. Along with the HVAC system, the building’s electrical and plumbing
systems will also need to be retrofitted to serve the new floors.
Lastly, the building’s structural system would need to be tested to determine if it can withstand the additional loads. To
continue with the adding of new floors would mean retrofitting and strengthening the structure. Additional supporting
structural systems may also be required. Buildings already designed with provisions for future additions can apply these
principles while making those additions.
6.3. Summary
A solar envelope is the largest volume that can be built on a site that allows solar access to neighbouring buildings for
specified hours every day. Most buildings have not been constructed to this standard and might cast shadows on
neighbouring sites. A digital tool was developed based on the solar envelope to allow additional volume to be added to
existing building geometry without casting additional undesirable shadows. Five building geometries were tested. The site
location and cut-off times were varied, solar envelopes were generated, and the change in building volume was calculated.
The amount of volume added varied with the location of the site and the desired cut-off times.
The principles were applied to a commercial neighbourhood in Los Angeles. The increase in usable floor area, without
changing the solar access of adjoining buildings, was calculated. More usable floor area was possible for buildings with
larger footprints and site areas. Addition of floors depend on construction costs, and the ability of building services and
structure to support the new floors. Installing PV systems, and building landscaping elements within the solar envelope are
alternative uses. This information could be part of zoning ordinances, controlling additions and renovations to existing
70

buildings not built within a solar envelope, to prevent additional shadows being cast as a result of additions and significantly
impacting the solar access of the surrounding buildings.
Solar envelopes principles are important for low- energy, passive architecture. With growing population and need for
expanding cities, it becomes important to renovate and upgrade existing buildings to cater to the needs of the future. In such a
scenario, the solar envelope for site with existing buildings is a tool that can be used for planning urban growth.
71

CHAPTER 7
7. FUTURE WORK
Solar envelopes for sites with existing buildings were studied. A digital tool was developed to generate solar envelopes. The
principles were then applied to an urban area and the results studied. Being limited in time, there are various areas in the
research that were not examined in detail. This chapter outlines a few areas that can be studied in the future. This include
further development of the digital tool, more research of envelope generation techniques for more cases than what was tested
here, and further study of urban applicability.
7.1. Add other features to the Dynamo tool for generating solar envelopes.
The Dynamo script currently only takes in rectangular sites as inputs. The site length and width are entered as inputs. To
increase the scope of applicability of the tool, other site geometries need to be incorporated. A possible area of work could be
modifying the script to take in site input directly from Revit. This would also reduce the number of items to be inputted by
the user.
Another feature that can be added is an option for sloped sites. Currently, the tool does not have any option for inputting site
slope values. However, as solar envelope generating principles for sloped sites already exists, they can thus be incorporated
into the tool. This feature will require at least two types of input (Section 2.4.3) – the site slope value, and the direction the
slope is facing (north, south, east or west). Both these parameters will influence the envelope shape.
Currently, the tool considers equal shadow fence heights. Only one value can be inputted as a shadow fence height for all
edges of the site. In practice, shadow fence height requirements can vary depending on the conditions of the adjacent sites.
The tool can be modified to include this aspect as well.
7.2. Test principles for other geometries.
Only two basic types of building geometries have been tested for solar envelopes – a rectangular geometry and an L-shaped
geometry. For a better understanding of how the solar envelope principles work and vary when used for sites with existing
buildings, it is important to test out an generate envelopes for other common building shapes. Building forms such as
buildings with courtyards, circular building forms and other curved forms can be studied to better understand solar envelope
geometries (Figure 71). It would be of particular interest to determine envelope forms for buildings with curved forms, as the
curved edges could affect the shape and the method of generation of building roof and side envelopes dramatically.

Figure 71 - Examples of other building geometries that can be studied, in addition to the rectangular and L-shaped
geometries studied.
In addition, the principles could be used to generate envelopes for sites which are non-rectangular. For this investigation,
only a rectangular site had been considered. The envelope geometry for the site will change with the site shape, and the way
this would affect the overall envelope shape can be studied.
7.3. Test other factors that affect solar envelope geometry
Only the effects of site location and desired cut-off times on envelope volume has been studied here. There are other factors
which affect the envelope geometry, as discussed in Section 2.4. The site dimensions and building form are factors that
affects envelope volume. These could be changed as discussed in the previous section. Site slope also influences envelope
volume. The effect of buildings on sloped sites on solar envelope geometry can be studied. An interesting study would be the
result of varying the site slope on the envelope volume.
Various building orientations could be studied as well. In this case, the test cases were considered to be oriented along the
cardinal directions. Changing the building and site orientations will affect the envelope being generated as discussed in
Section 2.4.2. The site and the roof envelopes would be affected as the envelopes will have less height and volume due to
change in orientation. Changing the orientation will also change the building sides that are always in shadow, thereby
affecting the building side envelope generation as well.
72

7.4. Further urban applications study
Further urban application studies can be done to determine feasibility of application. This involves applying the principles to
other cities and neighbourhoods. The neighbourhood studied in Los Angeles follows a street grid. Furthermore, every
building studied had a rectangular geometry. When the principle was applied to each building, the envelope generation
technique for every building was similar. For the principle to be universally applicable, other neighbourhood configurations
need to be studied. This include cities not planned on a grid, neighbourhoods consisting of different building and site
geometries, and neighbourhoods which are not just commercial (as studied here) but comprising of other uses as well.
Another study could focus on actual cost considerations. As discussed in Section 6.2, one of the constraints while applying
this principle is the cost of construction of additional floors and services. A detailed study can be done considering a
neighbourhood any a city of the cost of constructing these additions. This cost then can be compared with the income that can
be generated from the new spaces to determine if the additions are economically viable. This study needs to include cost of
maintenance of these spaces as well.
7.5. Chapter summary
Future research on this topic can include adding other features to the Dynamo tool, such as non-rectangular sites, a scope for
sloped sites, and an option for non-equal shadow fence heights. So far, only two building geometries have been studied for
this principles. Other geometries can be studied as well, such as rectangular building with courtyards, and circular and other
curved buildings.
Of the many factors that affect solar envelope geometry, only the effects of changing site latitude and cut-off times have been
studied. Varying the other factors and observing the results is an interesting future area of research. Lastly, further urban
applications studies need to be done to determine the feasibility of applying this principle in practice.
73

APPENDIX
A. The Dynamo script
For the purpose of this thesis, the script was modified and functions were added on. The main part of the script was kept the
same as described in Section 3.4. Functions such as volume and area calculations, divisions of the envelope geometry into
floors, generation of a side envelope were added to the main script (Figure 72). These functions were needed for this
investigation. Based on user requirements, similar modifications and additions can be made to the script to suit individual
purposes.

Figure 72 - Full Dynamo script with all add-ons
B. Inputs
The input units are very important for correct envelope generation. For exporting as a .sat file, there is an option to choose the
units, and the numbers entered here should be done accordingly. For the import directly to Revit option, the units have to
match that of the Revit file, hence the values entered here should be done accordingly.

74

C. Site boundaries
The equations used to calculate the coordinates for site edge points are described in Section 3.4.2.

D. Summer solar angles
The equations used to calculate the summer solar angles are described in Section 3.4.3.

75

E. Winter solar angles
The equations used to calculate the winter solar angles are described in Section 3.4.3.

76

F. Summer ridge points
The equations used to calculate the x, y, and z coordinates of summer ridge points are described in Section 3.4.3.

G. Winter ridge points
The equations used to calculate the x, y, and z coordinates of winter ridge points are described in Section 3.4.3.

77

H. Determination of envelope height

I. Geometry generation

78

J. Outputs
There can be four possible outputs based on the values of grid orientation and shadow fence being zero or not.

K. .sat output
Similar script for all four outputs.

L. Import directly to Revit

79

M. Side envelope generation

80

BIBLIOGRAPHY

Books -
Knowles, Ralph L. 1981. Sun rhythm form. Cambridge, Mass: MIT Press.
Dissertations –
Henkhaus, Alicyn E. "Computer-Generated Solar Envelopes And Building Information Modeling (BIM)". Masters,
University of Southern California.
Juyal, Manu. 2002. SolCAD: Three-dimensional spatial design tool to generate solar envelope. Ph.D. diss., ProQuest, UMI
Dissertations Publishing.
Topaloslu, Birol. Solar envelope and form generation in architecture. Ph.D. diss., METU
Yeh, Uen-Fang Patricia. 1992. Computer aided solar envelope design. Master’s thesis, ProQuest, UMI Dissertations
Publishing.
Papers and Journal articles –
Kensek, Karen, and Douglas Noble. 1998. Computer generated solar envelopes in architecture. The Journal of Architecture 3,
(2): 117-127
Knowles RL. The solar envelope. Solar Law Reporter. 1980; 2(2):263.
Knowles, Ralph L. 2003. "The Solar Envelope: Its Meaning For Energy And Buildings". Energy and Buildings 35 (1): 15-25.
Doi: 10.1016/s0378-7788(02)00076-2.
Knowles, Ralph L., Richard D. Berry, Solar Energy Research Institute, and Solar Energy Information Data Bank (U.S.).
1980. Solar envelope concepts: Moderate density building applications: Final report. [Golden, Colo.?] :Washington, D.C.
:Springfield, Va: Solar Energy Information Data Bank ;Available in print from Supt. of Docs., U.S. G.P.O. ;Available in
microfiche from National Technical Information Service
Knowles, Ralph L., and Karen M. Kensek. 2005. "The Growing Need For Solar Access Zoning". Proceedings Of The 2005
Solar World Congress, Orlando FL.
Niemasz, Jeffrey, Jon Sargent, and Christoph F Reinhart. 2013. "Solar Zoning And Energy In Detached Dwellings".
Environment And Planning B: Planning And Design 40 (5): 801-813. doi:10.1068/b38055.
Paramita, Beta, and M. Donny Koerniawan. 2013. "Solar Envelope Assessment In Tropical Region Building Case Study:
Vertical Settlement In Bandung, Indonesia". Procedia Environmental Sciences 17: 757-766.
doi:10.1016/j.proenv.2013.02.093.
Vartholomaios, Aristotelis. 2015. "The Residential Solar Block Envelope: A Method For Enabling The Development Of
Compact Urban Blocks With High Passive Solar Potential". Energy And Buildings 99: 303-312.
doi:10.1016/j.enbuild.2015.04.046.
Vonderohe, Alan P. 1986. Geometry of solar envelopes. Journal of Surveying Engineering 112, (1): 3-17
Websites -
"Daylighting Strategies | U.S. Green Building Council." Daylighting Strategies | U.S. Green Building Council. Accessed
August 30, 2015. http://www.usgbc.org/education/sessions/daylighting-strategies-4775236
"Daylighting." Daylighting. Accessed August 30, 2015. http://www.wbdg.org/resources/daylighting.php
"Design." Heat Transfer Through Windows ›› SeeBeyond – Do You Really Know What Windows Can Do? Accessed August
24, 2015. http://www.seebeyondwindows.com.au/design/heat-transfer/.
"Heat Energy Flows in Buildings | Sustainability Workshop." Heat Energy Flows in Buildings | Sustainability Workshop.
Accessed August 30, 2015. http://sustainabilityworkshop.autodesk.com/buildings/heat-energy-flows-buildings.
81

"Heat Energy Flows In Buildings | Sustainability Workshop". 2016. Sustainabilityworkshop.Autodesk.Com.
http://sustainabilityworkshop.autodesk.com/buildings/heat-energy-flows-buildings.
Knowles, Ralph L. "The Solar Envelope". Www-Bcf.Usc.Edu. http://www-bcf.usc.edu/~rknowles/sol_env/sol_env.html.
McCann Kettles, Colleen. "A Comprehensive Review of Solar Access Law in the United States - Suggested Standards for a
Model Statute and Ordinance." Solar America Board for Codes and Standards. October 1, 2008. Accessed October 27, 2015.
http://www.solarabcs.org/about/publications/reports/solar-access/pdfs/Solaraccess-full.pdf.
"Passive Solar Design". 2016. Passive Solar Design. http://passivesolar.sustainablesources.com/.
"Solar Rights: Access to the Sun for Solar Systems." Rights to the Sun - Go Solar California. Accessed October 28, 2015.
http://www.gosolarcalifornia.ca.gov/solar_basics/rights.php.
"The Sun's Position." The Sun's Position. Accessed August 31, 2015. http://www.pveducation.org/pvcdrom/properties-of-
sunlight/suns-position
Watson, Donald: Time-Saver Standards for Urban Design. The solar envelope, Chapter (McGraw-Hill Professional, 2003),
AccessEngineering

Abstract (if available)

Abstract A solar envelope for a site is the largest volume that can be built that allows solar access to neighbouring buildings for a specified period of time in a day (Knowles 1981). Solar envelope principles are important for low-energy, passive architecture on the neighbourhood scale. The concept and generation of a solar envelope is based on the daily and annual movement of the sun across the sky, which defines the maximum buildable volume for a building while still allowing solar access for neighbouring buildings. When applied as a zoning tool over a neighbourhood, solar envelopes ensure solar access for all buildings. With guaranteed access to sunlight, designers can choose to use that resource for daylighting, energy generation, and passive heating (Knowles 1980). Buildings that have already been built without considering solar envelope constraints might cast undesirable shadows on neighbouring sites. Any additions made to such a site and the building geometry may result in additional shadow being cast on to the surroundings. Using similar principles to those used to generate solar envelopes, how much more can be added to the existing building geometry without casting additional shadows beyond the site has been determined. For this purpose, a solar envelope generation tool has been created in Dynamo, to work with Revit, based on user input. User inputs are site location (latitude and longitude), envelope cut-off times, site grid orientation, and shadow fence. Five building geometries were tested – a rectangular geometry, and four L-shaped geometries in different orientations. The site location (latitude and longitude) and envelope cut-off times were varied in each case, solar envelopes for the sides of the building were generated, and the change in building volume was calculated. The principles were then applied to 6 blocks in a commercial district of Los Angeles, and the increase in floor area ratios (without further impacting solar access of the surrounding buildings) was calculated. The test cases were modelled in Revit as conceptual masses. Solar envelopes, whenever required, were generated using the tool and imported into Revit. Additional volumes were also modelled in place on the test cases as conceptual masses. Results show that typically additional volume is possible that does not cast additional shadows within the specific time of the day. The amount of volume added changes with the location of the site and the desired cut-off times. This information could be part of zoning ordinances, controlling additions and renovations to existing buildings not built within a solar envelope, to prevent additional shadows being cast as a result of additions. Conversely, these principles could be used by existing buildings to make renovations and additions to the building geometry, without further impacting the solar access of the surrounding buildings.

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Asset Metadata

Creator Bhattacharjee, Shinjini (author)

Core Title Pushing the solar envelope: determining solar envelope generating principles for sites with existing buildings

School School of Architecture

Degree Master of Building Science

Degree Program Building Science

Publication Date 04/20/2016

Defense Date 03/21/2016

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

Tag OAI-PMH Harvest,passive architecture,solar access,Solar energy,solar envelope,sustainable architecture

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Noble, Douglas (committee chair), Kensek, Karen M. (committee member), Schiler, Marc E. (committee member)

Creator Email shinjinb@usc.edu,shinjini.bhattacharjee92@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c40-234548

Unique identifier UC11276461

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Document Type Thesis

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Rights Bhattacharjee, Shinjini

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

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