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Research Article Building Thermal, Lighting,
and Acoustics Modeling
E-mail: francesco.deluca@taltech.ee
A novel solar envelope method based on solar ordinances for urban
planning
Francesco De Luca1 (), Timur Dogan2
1. Tallinn University of Technology, Department of Civil Engineering and Architecture, Ehitajate tee 5, Tallinn 19086, Estonia
2. Cornell University, College of Architecture Art and Planning, 240 E. Sibley Hall, Ithaca, NY 14853, USA
Abstract
Solar access requirements constitute a significant aspect for the performance of buildings and for
the image of cities. The solar envelope is a method used during the schematic design phase to
determine the maximum volume that buildings cannot exceed to guarantee good access to direct
sunlight in streets and on neighboring facades. However, two major shortcomings exist that
prohibit the use of existing solar envelope techniques in practice: They don’t include the
neighboring buildings in the overshadowing calculation, and they utilize a fixed start-and-end
time inputs for the selection of specific hours of direct solar access. Different direct solar access
ordinances exist that require that new buildings do not obstruct direct sun light in existing
dwellings: (1) during specific hours, (2) for a quantity of hours, (3) as a fraction of the actual solar
access. For the second and third type of ordinances no existing solar envelope methodologies
exist. The research presented in this paper develops a computational method that increases the
efficacy of the generated solar envelopes including the context in the calculations and provides
the possibility to select the quantity and quality of sun light hours, and thus allows the modeler to
generate solar envelopes optimized for different objectives. The method aims to help architects
and planners to design environmental conscious buildings and urban environments.
Keywords
urban planning,
building performance,
solar envelope,
direct solar access,
environmental design,
computational design
Article History
Received: 8 November 2018
Revised: 2 April 2019
Accepted: 22 May 2019
© Tsinghua University Press and
Springer-Verlag GmbH Germany,
part of Springer Nature 2019
1 Introduction
Solar access provision can significantly influence urban form
and character of cities. Throughout history, humans have
used natural light as a form-giver. Besides just illuminating
streetscapes and interior spaces, designers use sunlight to
emphasize building volume organization, to generate surface
contrast for improved space perception and favoring
meditation in sacred spaces. The special attention given to
natural light in the design process is demonstrated by several
recommendations and building regulations that have been
published over the years.
The most emblematic regulation in this regard is the New
York Zoning Resolution of 1916. The floorplan of a building
could have been the same as the footprint up to a height of
about 30–40 meters. Beyond this point it was required to
recede gradually to a floor area 25% the size of the footprint
and use that ratio for the highest mass of the building
(Willis 1995). This regulation was introduced to safeguard
an adequate level of daylight in the street canyon and resulted
in many terraced and ziggurat-like buildings that shaped
the skyline of New York of the time (Fig. 1). Further, the
Doctrine of Ancient Lights is an English Common Law of
1663 still in use through the Rights to Light Act of 1959.
The regulation states that windows that have received a
certain amount of sun light over a period of 20 years, have
the right of an easement on neighboring lands. Although this
rule doesn’t per se generate a characteristic building shape,
it tends to favor urban variety and buildings fragmentation
(Howard 1989). Another example is the iconic plan for the
city of Barcelona of 1859 by Ildefons Cerdà. It features regular
array of quadrangular blocks located at a specific distance
to be occupied only on two sides with orientation NE-SW
or NW-SE to deliver adequate quantity of natural light and
ventilation (Coch and Curreli 2010). In Ancient Greece
solar access has been used as a principle in urban planning
BUILD SIMUL
https://doi.org/10.1007/s12273-019-0561-1
De Luca and Dogan / Building Simulation
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Fig. 1 The Chrysler Building and Midtown Manhattan in New
York City, ca. 1932
influencing buildings orientation, height and distance to
improve comfort and healthy living conditions (Butti and
Perlin 1980). In his The Ten Books on Architecture, Vitruvius
recommend that houses in northern countries should have a
“warm exposure” and in southern countries “must be built
more in the open and with a northern or north-eastern
exposure” (Morgan 1914).
Sun light used to be the primary resource to illuminate
the interior of buildings until the end of the first half of
twentieth century, when energy for electric illumination
became cheap and luminaires affordable. Building layouts
and facade designs did not have to be related anymore
and in some exceptional cases buildings were not featuring
windows (Collins 1976). Appropriate use of sun light in
interiors regained importance during the 1970s due to the new
awareness about finite resources triggered by the oil crisis.
In recent years, daylighting has reemerged as interesting
research topic due to energy efficiency concerns (Reinhart
and Selkowits 2006), its positive relation with workplace
performance and health (Andersen et al. 2012), its non-visual
effects such as the entrainment of circadian rhythm and the
improvement of physiological and psychological well-being
of humans (Lockley 2009; Altomonte 2008) as well as
architectural quality resulting in new metrics and analysis
workflows (Dogan and Park 2019; Saratsis et al. 2017). Studies
also show that natural light is the most appreciated source
of illumination of building interiors by occupants as it provides
accurate color rendering and is often associated with good
visual connections to the outside. Daylight is composed by
direct sun light and diffuse light. Although the light diffused
by the sky, and the one reflected by the environment is an
important factor for illuminating building interiors, direct
sun light is the most appreciated for its quantity, quality
and distribution potentialities (Reinhart 2014; Johnsen and
Watkins 2010).
Natural light access requirements for planning and
building construction are different from country to country
and in some cases may even differ between regions or cities.
Given that there is such variety in the regulation it is helpful
categorize existing ordinances into two main groups: Implicit
(land use) and explicit (quantity of natural light) regulations.
Implicit or land use ordinances often require setbacks
from the property lines or height/street width ratios. These
ratios are often criticized for not taking into account site
specific parameters and environmental factors that are
important inputs for the accurate prediction of sunlight
access (DeKay 1992). Therefore, the land use prescription
often cannot guarantee appropriate daylighting levels and
solar access or may be overly restrictive.
Explicit ordinances prescribe required quantities of
natural light and thus can ensure that a dwelling unit or
space has access to adequate levels of sunlight. Explicit
ordinances distinguish between diffuse daylight and direct
sun light on building windows. Interior diffuse daylight
makes use of static metrics such as Daylight Factor that
predicts if a room will have adequate natural illumination
depending solely on room and windows size, material
properties and external obstructions (Waldram 1923), or
metrics such as Spatial Daylight Autonomy that takes into
account location, climate and building orientation using
annual daylight simulations (Reinhart 2015).
The ordinances based on direct sun light take into account
the location of the dwelling and the surrounding environment.
They require a duration of hours during which direct sun light
hits a window of a room. This calculation is a geometric
analysis that does not account for cloud cover and sky
condition. The so called direct solar access is the most
compelling among the explicit type of requirements. Its
fulfillment is challenging as the sun could barely be visible
from some building orientations (i.e. north in the northern
hemisphere) depending on the latitude and period of the
year and it could be blocked by surrounding buildings.
Additionally, compliance checks during the design phase
are complicated due to tool limitations that are described in
the next section. Compliance with interior daylight regulations
are easier to accomplish as they take into account the diffuse
lighting contributions by the sky and reflections from the
environment and surrounding buildings.
The solar envelope (SE) method, introduced by Ralph
Knowles, is a geometric evaluation approach that can be used
during the schematic design phase. It establishes the maximum
volume and heights that new buildings should not exceed in
order to prevent overshadowing of neighboring dwellings
(Knowles 1981, 2003). To date, different tools to calculate SE
volumes exist. However, two major shortcomings prohibit
the use of existing SE techniques in practice: They don’t
include the neighboring buildings in the overshadowing
calculation, and they utilize a fixed start-and-end time as
De Luca and Dogan / Building Simulation
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input for the selection of the analysis period.
However, the different direct solar access ordinances
that exist require that new buildings do not restrict direct
sun light access for existing buildings: (1) during specific
hours, (2) for a certain amount of time, and (3) as a fraction
of the actual solar access on site. For the first type existing
tools can be used effectively, however, for the second and
third type of ordinances no existing SE methodologies exist.
This paper hence proposes a new method for the generation
of SEs that is based on Knowles’ initial method but that
also tackles the mentioned limitations to facilitate the use
of SEs by planners and architects for regulatory compliance
checks during the design process.
2 Background
Direct solar access is regulated in different ways depending
on the specific country’s requirement. In Table 1 the most
prominent regulations and standards regarding direct solar
access are listed.
Although Table 1 is not all-encompassing, it lists many
representative regulations that can be categorized in mainly
three different types:
Type 1 – Ordinances that require specific hours or a
specific time period during the day (the cities of Boulder
and Ashland in the US).
Type 2 – Ordinances that require a quantity of hours
during the day (Czech Republic, Slovenia, Poland, Slovakia,
Germany and China).
Type 3 – Ordinances that require a ratio or percentage of
the actual quantity of direct solar access during the day
(UK and Estonia).
The SE method can be used in relation to the mentioned
direct solar access ordinances to determine the massing
of new buildings that have to respect the solar rights of
neighboring dwellings. To calculate a SE the following inputs
are required: Latitude of the location, size and layout of
the plot on which the SE is to be created, distances of the
neighboring facades to take into account, height of the shadow
limits, daily hours and period of the year during which solar
access must be guaranteed.
The SE can be calculated by hand using sun charts
Table 1 Direct solar access regulations and standards
Country/city Regulation Definition Type
US/Boulder
(CO) Solar Access Guide. Section 9-9-17, BRC 1981
(City of Boulder 1981)
New buildings cannot cast shadows on surrounding facades above the
shadow line, the height of which is different depending on the Solar Access
Area (Area I 12 ft, Area II 25 ft, Area III no shadow line) between 10:00 and
14:00 on 21.12
1
US/Ashland
(OR) Solar Access. Land Use Ordinance 18.70 (City
of Ashland 2011)
New building cannot project a shadow taller than 6 ft on the most northern
point of its own property line during the winter solstice at 12:00, that at the
latitude of 42°11ʹ North correspond to a sun altitude angle of about 24°,
protecting in this way the neighboring properties
1
Czech
Republic Regulation 268/2009 and Standard CSN 73
4301:2004 (Darula et al. 2015) Direct solar access of minimum 1.5 hours on 01.03 or an average of 1.5 sun
light hours per day in the period between 10.02 and 21.03 2
Slovenia Technical Guidelines TSG-1-004:2010 “Efficient
energy use” (Košir et al. 2014) Direct sun light for at least 2 hours on 21.12 and 4 hours on 21.03 and 21.09
and 6 hours on 21.06 2
Poland Minister of Infrastructure Regulation, 2002
(Sokol and Martyniuk-Peczek 2016)
Permanently occupied rooms in premises have to receive minimum 3 hours
of direct solar access between 7:00 and 17:00 on 21.03 and 21.09 and 1.5 hours
in at least one room in case of multi-family apartments 2
Slovakia Building Standard STN 73 4301, 1998 (Hraska
2004)
Windows of one third of apartment living area should receive at least 1.5 hours
of direct sun light, calculated on a point centered on the glazing at 1.2 m
from the floor, for every day of the period between 01.03 and 13.10 2
Germany Regulation DIN 5034-1 (German Institute
for Standardization 1999) In a dwelling at least one window need to receive minimum 1 hour of direct
sun light on 17.01 and 4 hours on 21.03 and 21.09 2
China
Code of Urban Residential Areas Planning &
Design - Construction standard No. 542
(Ministry of Construction of China 1993;
Geng et al. 2012)
The standard for residential buildings requires minimum insolation hours, 2
and 3 on the “Great Cold Day” (20.01) and 1 on the winter solstice,
depending on the size of the city (metropolitan, medium and small) and in
which climate zone it is located
2
UK BS 8206-2:2008. Lighting for buildings. Code
of practice for daylighting (BSI 2008)
A room window should receive during all the year at least 25% of the Annual
Probable Sunlight Hours (APSH). 5% of the required direct sun light should
be accessed during autumn and winter from 21.09 to 21.03 3
Estonia Standard “Daylight in dwellings and offices”
EVS 894:2008/A2:2015 (Estonian Centre for
Standardization 2015)
Existing premises cannot be deprived for more than 50% of their actual
direct solar access hours by new buildings for every day of the period between
22.04 and 22.08 3
De Luca and Dogan / Building Simulation
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indicating the sun azimuth and sun altitude during the
required hours of the days for the given location. Using
physical models, it is possible to test the calculated SE with
a Heliodon (Lechner 1991). Nonetheless the calculation by
hand is a very tedious and error prone procedure. Charts
are available with indication of the horizontal angles of the
ridges and the vertical angles of the slopes of the SEs
(Brown and DeKay 2001). The use of charts is very limited
since it can cover only a number of basic cases of plot
layout and orientation, neighboring building distances and
latitudes.
Computer software to automatically generate SEs has
been developed since decades. Pioneering computer tools
had very basic functionalities that made them difficult to use
in the design process. SolVelope permitted to generate SEs
selecting the orientation of a rectangular and horizontal
plot, the distance from surrounding buildings, the latitude
and the required period and hours (Yeh 1992). SolCAD
introduced the possibility to import CAD files of the plot
layout and neighboring building footprints, with the possibility
to use different heights for the shadow lines of the
surrounding buildings (Juyal et al. 2003). CalcSolar used
rectangular and horizontal plots, different cut-off time
expressed as start and an end hour for different days,
different shadow boundaries with different heights and was
available in AutoCAD as an AutoLisp routine (Noble and
Kensek 1998). SustArc permitted to calculate the Solar Rights
Envelope and introduced the additional possibility to calculate
the Solar Collection Envelope (Capeluto and Shaviv 1999,
2001). The latter predicts the minimum heights at which
new building windows should be located to receive the
required quantity of direct solar access using the additional
input of surrounding building roof lines.
Software developed in more recent time lacked either
important functionalities or was not well integrated in design
software. The tool BlockMagic, integrated in the decision
support system for urban planning CityZoom, permitted to
take into account solar access of buildings surrounding the
plot under development through obstruction angles which
were used to determine setbacks at determined distances from
the plot outline and relative maximum height of buildings
(Turkienicz et al. 2008). The SE tool available in the
environmental analysis software Ecotect Analysis permitted
to evaluate the overshadowing of a development on a close
property by using planes extruded from the property line
toward the sun at selected vertical angles (Marsh 2003). A
tool to be used in the BIM software Revit has been developed
to generate SEs using the method of cutting solids (Kensek
and Henkhaus 2013). Volumes generated from shadow fences,
located on site boundary or on surrounding properties also
at different height, were subtracted from an extrusion of
the plot of any polygonal shape. Though the method offered
great flexibility, as time requirement it was possible to use
only symmetric hours before and after noon on summer
and winter solstices.
Custom tools to generate SEs are developed for specific
studies. A research about whole energy assessments of single-
family residential developments used SEs obtained through
extrusion of the plot contour in the direction of specific sun
light hours and days of the year and consequently calculating
the intersection of all the extrusions (Niemasz et al. 2011).
The Residential Solar Block envelope, generated using
intersection of the extrusion of the building block, volumes
extruded from solar volume boundary toward relevant sun
directions and solar fan volume to prevent self-shadowing,
showed potentialities for determining optimal layouts of
compact blocks with high solar exposure (Vartholomaios
2015).
Nowadays it is possible to generate SEs in very early stages
of design using tools such as Ladybug Tools and DIVA4
(Sadeghipour and Pak 2013; DIVA 2017) that are integrated
in the popular parametric and algorithmic design software
Grasshopper for Rhinoceros (McNeel 2017a,b). Although
specific inputs may vary from tool to tool, a core set of
necessary inputs is consistent across the board including
the plot layout, location latitude, and most importantly a
fixed start-and-end hour time input (e.g. at noon, from
10:00 to 14:00) for every day of the indicated period for the
generation of the SE. The latter limits current tools so that
they can only effectively generate SEs for ordinances of Type 1.
The first type of ordinances presented in Section 2 is the
only one that uses specific hours or a fixed start- and-end
hour of direct solar access during the required days.
In an urban environment, different facades of buildings
such as those surrounding a plot on which a SE has to be
calculated, have different orientations and are obstructed in
different ways by the surrounding environment. Thus, the
facades and even portions of them receive different quantities
of direct solar access hours during different hours of the
days of the required period (Fig. 2). Generating a SE that
factors in these temporal and spatial differences is however
not feasible using existing software tools. These temporal
and spatial differences are important parameters that become
relevant if the site is within regulatory bounds of ordinances
of Type 2 and Type 3. These require specific quantities of
direct solar access hours hence at first a calculation of the
hours during which a facade or a portion of it has access
to direct sun light has to be performed and consequently a
selection of the hours is required. Recent research has
developed workflows that include sun light hours calculations
on existing facades permitting sun light hours selection
in the generation of SEs to propose improvements of the
available software tools (De Luca 2016; De Luca and Voll
2017).
De Luca and Dogan / Building Simulation
5
Fig. 2 Analysis of daily minimum sun light hours between 22.04
and 22.08 on buildings in the city of Tallinn
This paper introduces a method for the generation of
the SEs that expands the mentioned recent research by
developing a SE algorithm that overcomes the shortcomings
of existing methods, i.e. it is efficient in urban environments
and for all the three types of ordinances, and add func-
tionalities, i.e. permits the selection of different SEs shape
and size. The method is under development as a set of free
software tools that are expected to be distributed as an
environmental analysis and design Grasshopper plug-in to
be available to a vast number of designers involved in
urban design.
3 Methods
The new proposed method allows the generation of SEs
that can take existing contextual geometry, direct solar
access hours per day and associated incident solar radiation
on building facades into account. This enables modelers to
strategically select specific performance goals and timeframes
when direct solar access is of importance to the design
project. Including the option to indicate a fixed start-and-
end hour as the existing software, the new method is hence
suitable for all three types of ordinances. In the following
sub-sections, a detailed description of the methodology and
its implementation in Grasshopper for Rhinoceros is given.
The method is developed and validated through parametric
and environmental design tools present in the plug-in
Ladybug Tools and DIVA4 and by custom components
realized by the authors (in algorithmic design a component
is a tool performing a function). The flow chart of Fig. 3
shows the method steps and the algorithm components.
3.1 Facades selection and subdivision
In a preliminary step the existing facades affected by the
possible overshadowing of the new buildings are selected
through a first custom component. The contextual buildings
(or other obstructers) are modeled as polysurface geometry
of arbitrary complexity. The building plot is indicated by a
closed polyline. Areas of interest in the solar analysis, such
as facades, parks or sidewalks are provided in form of an
analysis grid that subdivides selected analyses surfaces.
These discretized analysis grids are used to construct the so
called “shadow fences” (Knowles 1981), that represent the
Fig. 3 Flowchart of the new method and algorithm components. White boxes: existing parametric and environmental design tools. Gre
y
boxes: custom components and tools realized through visual scripting by the authors
De Luca and Dogan / Building Simulation
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lowest edges of the surfaces that need to receive a certain
amount of direct sunlight, i.e. the facade portions used to
calculate the direct solar access and the incident solar
radiation (Fig. 4).
3.2 Month/day/hour selection
After the preparation of the 3D model the first step for the
generation of the SE is the selection of the analysis period
in the form of start-and-end month/day/hour to indicate the
days of the year and the hours that is needed to take into
account.
For the ordinances of Type 1 it is possible to select the
days and hours required, i.e. for Boulder (CO) the selection
is month 12, day 21 and hours from 10:00 to 14:00. For the
ordinances of Type 2 the selection is either all the 24 hours
or a start-and-end timeframe during which it is possible
select the quantity of hours required, i.e. for Poland are
selected month 03, day 21 and month 09, day 21, and the
hours from 7:00 to 17:00 for both days. For ordinance of
Type 3 the selection is always the 24 hours for the required
day or days of the period, i.e. for Estonia the selection is
from month 04, day 22 to month 08, day 22, and the hours
from 01:00 to 24:00 for all 123 days. For ordinances of Type 1
all hours during the indicated timeframe are required. For
ordinances of Types 2 and 3 only a portion of the indicated
timeframe is required. All 24 hours are selected for ordinances
of Type 3 because it is not known a priori when the sun
light is available on the existing facades during every required
day and the proposed tool automatically filters out times
where the sun is below the horizon.
Given the selection of the hours, the next step is to
indicate the preferred time-step (ts) for a subdivision of the
hours in minutes or group of minutes (e.g. ts2 = 30 minutes,
ts6 = 10 minutes), to obtain higher accuracy calculations
for the SE generation. The result is a list (hierarchical by
day) of all discrete time steps within the selected analysis
periods.
In the following algorithmic step, the hours and time-
steps are used to generate the sun vectors (sun light hours/
fractions) during daytime on the basis of the required location
Fig. 4 The facades selected and subdivided in samples. The samples
used for the solar envelopes generation
input of latitude, longitude and time zone. If available, the
location input can be obtained from an EPW (EnergyPlus
Weather Data) weather file.
3.3 Direct solar access hours and incident solar radiation
The proposed new method needs to take into account the
different quantity of direct solar access hours and incident
solar radiation that the facades and portion of facades
(samples) receive in an urban environment. The direct
normal solar radiation data is obtained by the possibility to
read as input the EPW weather files. Existing methods for
SEs generation usually only compute direct sun light hours
omitting important information. For example, different
sun directions (i.e. in early morning or at noon) can be
very different in terms of energy and facade incidence
angles influence consistently the quantity of solar radiation
brought to the premises (Ratti and Morello 2005). The
proposed method includes the possibility of solar radiation
calculation as performance criterion for SE generation.
Direct normal radiation levels are readily input data available
in EPW files in hourly resolution for many locations
globally.
A second custom component, uses sun vectors as input
and tests sun visibility from each facade sample for every
time-step using a Mesh Ray intersection method provided
by the Rhino Grasshopper. The component returns a Boolean
pattern that indicates for each facade sample a “True”
statement if the following three conditions are fulfilled:
(1) The angle between the sun vector and the sample normal
is smaller or equal than 80°; (2) The sun vector does not hit
any context building; (3) The sun vector elevation angle is
larger than 10°. Otherwise a “False” statement is returned.
The first condition is implemented to exclude sun vectors
with an angle larger than 90° with the sample normal which
are not visible by the facade and has been used 10° as dead
angle because sun vectors with angles larger than 80° do
not penetrate the building due to wall thickness (Darula
et al. 2015). The second condition ensures that direct sun
light potentially visible by the sample is not blocked by
surrounding buildings and the third condition guarantees
that the sun vectors are not blocked by buildings of the
farther surrounding urban environment or terrain variations.
All thresholds mentioned above are defaults that can be
overridden by users in the new algorithm. The second
custom component of the algorithm calculates the quantity
of visible sun vectors for each sample for every day and
pairs it with data of vector’s vertical angle and incident solar
radiation. The solar radiation incident the sample is calculated
using the data from the weather file and Lambert’s cosine
law (Smith 2000).
De Luca and Dogan / Building Simulation
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A third custom component evaluates if each sun vector
passes through the plot on which the SE will be built using
a hit-or-miss analysis on a volume extruded from the plot.
Additionally, the algorithm calculates the distance from the
plot corners of the sun vectors passing through the plot.
This last test is useful to give the designer additional options
for the performance of the SE to generate i.e. to increase
the SE size or to determine the location of the maximum
height (De Luca 2017).
The developed method thus calculates the quantity of
direct solar access hours (including time-steps) for every
sample during every day of the required period and the
expected solar radiation associated with each sun vector on
the facade sample. Recent research proposes a new framework
for daylight evaluation inside residential dwellings considering
weather data (Dogan and Park 2017) and another takes into
account data of global horizontal radiation for the generation
of SEs (Capeluto and Plotnikov 2017). The novelty of
the present method is that it considers the incident solar
radiation calculated from weather data, in addition to quantity
of sun light hours, on the facade samples to efficiently
generate SEs for the ordinances of Type 2 and Type 3.
3.4 Sun vectors selection
A fourth and fifth custom component, the core of the
developed method, determine the SE shape through the
selection of sun light hours (sun vectors). For the ordinances
of Type 1 this selection is not needed since the month/
day/hour selection indicates exactly the required sun light
hours to use in the generation of SEs. For ordinances of
Type 2 and Type 3, the new algorithm permits to select the
most relevant sun vectors on the basis of selection options
presented in the following sections. The developed method
allows for two types of sun vector selection, a quantitative
selection and a qualitative selection.
3.4.1 Quantitative sun vector selection
The first type of selection permits to indicate the quantity
of sun light hours (sun vectors) required with three options:
(1) all; (2) quantity; (3) percentage. Option 1 is used for the
ordinances of Type 1 when indeed there is no possibility
of selection. All the sun vectors generated through the
month/day/hour selection are used. Option 2 permits to
indicate an exact quantity of sun vectors for each day or
different quantities for different days. This option is used
for ordinances of Type 2. Option 3 permits to select a ratio
of the sun vectors visible by each facade sample every day
of the required period, as required by ordinances of Type 3.
3.4.2 Qualitative sun vector selection
The second type of selection is possible only for Options 2
or 3 of the previous step of quantitative sun vector selection.
The qualitative selection takes a second pass at all selected
sun vectors from the quantitative selection routine and
evaluates additional characteristics attached to each sun
vector or time step to emphasize the envelope performance
that the designer wants to take into account. The sun vector
characteristics are the vertical angle (sun altitude), the
incident solar radiation, the trajectory, i.e. if the sun vector
pass or not through the plot and the distances from the plot
corners of those passing through the plot. The fifth custom
component allows for 5 methods of qualitative sun vector
selection which maximize either the SE size or the sun light
quality on the surrounding facades or permit trade-offs and
explorations of different SE forms (Table 2).
The maximization of the SE size of Method 1 is
guaranteed by the use of sun vectors with the largest sun
altitude that allows larger height displacement of the plot grid
points used for its construction (De Luca and Voll 2017).
Method 2 maximizes the quality of sun light selecting the
sun vectors/ time steps with larger incident solar radiation at
the expense of the SE volume. Larger solar radiation is
associated with sun vectors with narrow incidence angle
with the building facades, i.e. with sun vectors almost
perpendicular to the facade. The presence in the urban
model of facades facing east and west generates small size
SEs being the morning and afternoon sun characterized by
small elevation angle.
Trade-off between the methods that maximize either
SE size or sun light quality and optimization of the SE for
maximum buildout volume is possible using Methods 3, 4
and 5. Using these methods the necessary sun vectors are
selected firstly from rays that never cross the plot, to
minimize the quantity of sun vectors affecting the SE, and
secondly, if additional sun vectors are needed to reach
the required quantity of sun light hours, these are selected
among those passing through the plot. The sun vectors are
selected from outside the plot starting from the one with larger
vertical sun angle and consequently all the others with
progressively smaller values. Another option is to select the
sun vectors from outside the plot using the solar radiation
criteria, starting from the one with larger incident solar
radiation. During extensive tests, the two options did not
produce significant differences in SE size due the fact that
the sun rays passing outside the plot are seldom enough to
meet the required quantity of direct sun light hours so in
most of the cases all of them are selected.
Methods 3, 4 and 5 increase the size of the SE respectively
of the basic Methods 1 and 2. Method 3 is the one that
generate the larger SE of all. Method 4 is a trade-off between
Methods 1 and 2. It increases the size comparing Method 2
while still guaranteeing large incident solar radiation.
Method 5 permits to cut the SE on the corners to leave the
core free to reach the maximum allowed height, giving the
De Luca and Dogan / Building Simulation
8
designer also the possibility to opt for an unprecedented
formal selection (De Luca 2017).
3.5 Solar envelope generation
The selected sun vectors for every day of the required
period are used by an existing environmental design
component to generate a SE for each facade sample using
the existing method (Knowles 1981). It divides the plot in a
grid of points and for every sun vector that hit the facade
sample the height is calculated at which it passes in
correspondence of the grid point that is consequently
translated vertically for an equal height (Fig. 5).
A final custom component generates the resultant SE
shape merging all those calculated. Each SE associated with
every sample is constituted by the same number of translated
points that share the same X and Y coordinates and that
have different Z coordinates. The custom component selects
the smallest Z coordinate value for each set of points with
the same X and Y coordinates. In this way it is possible to
Table 2 Solar envelope generation methods and performance maximization or trade-off. The sun vectors are relative to one of the facade
samples used as analysis surface
# Method
SE
size
Light
quality
Trade-
off
1 Larger sun vertical angle
●
2 Larger incident solar radiation
●
3
Sun vectors from outside the plot with
larger elevation angle - Sun vectors
through the plot with larger elevation
angle
● ●
4
Sun vectors from outside the plot with
larger elevation angle - Sun vectors
through the plot with larger incident
solar radiation
● ●
5
Sun vectors from outside the plot with
larger elevation angle - Sun vectors
through the plot closer the plot corners
● ●
De Luca and Dogan / Building Simulation
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guarantee that the resultant SE will satisfy the direct solar
access of all the samples thus of all the surrounding facades.
The selected groups of points are used by the custom
component to generate the triangulated mesh of the upper
surface and the vertical sides and bottom of the final SE.
4 Case studies
To test the new SE method and the potentialities of sun
light hours selection, different case studies for the three type
of ordinances have been investigated, the generated SEs
validated, insolation and solar radiation performance of the
surround facades analyzed.
To validate the method and assess the provided solar
access on the surrounding facades the following analyses
have been performed:
Percentage of facade samples with the required direct solar
access among those that are receiving sufficient sun light
hours of insolation in the existing situation.
Average sun light hours reduction per facade sample for
entire days of the analysis period.
Total sun light hours reduction on all the samples for
entire days of the analysis period.
Average incident solar radiation reduction per sample
for entire days of the analysis period.
Average total (direct, diffused and reflected) solar radiation
reduction per sample for entire days of the analysis period
(to test variation of influence of sky and surrounding
environment).
The tests have been conducted for the required period
and additionally for the entire year, for the typical hot week
and the typical cold week. The scope is to analyze sun light
hours and solar radiation variation on surrounding facades
for periods different than those of the regulation. For the
calculation of solar radiation incident on the building
facades, an available environmental design component was
used. For total cumulative solar radiation, simulations are
performed through DIVA4 Radiation Map tool which uses
the cumulative sky method (Robinson and Stone 2004), and
the validated daylight simulation software Radiance (Ward
1994). The solar radiation simulation parameters are presented
in Table 3.
For all the sun light hours and solar radiation analysis
results are presented as the unitless remaining percentage
comparing the existing situation (without SE) not as the
quantity that has been reduced. For the three case studies an
urban environment constituted by buildings surrounding
a plot of 90 m by 90 m has been modeled. The plot is
subdivided with a grid of points at 4.5 m of distance for the
generation of the SE mesh. Smaller distances would increase
the accuracy of the envelope shape at the expenses of
significant longer computation time. Performance results
using different parameters for time resolution and grid size
for the SE generation are presented in section Discussion.
4.1 Ordinances of Type 1
To showcase the new SE method for a Type 1 ordinance,
the city of Boulder, Colorado (Lat. 40.01° N, Lon. 105.27° W)
has been chosen. An urban environment characterized by
buildings at slightly non uniform distance from the plot has
been created. The facades facing the plot have been selected
and subdivided in samples with size of 3 m by 3 m. The
rows of samples that have been used as shadow fences have
been located at a height of 3.66 m (12 ft) measured from
the sample center to the ground (Fig. 6). The selected rows
of samples constitute the shadow fences of the new method.
The assumption is that if the required sun light access is
satisfied on the shadow fences then all the above facade
segments will receive the required direct solar access
(Knowles 1981). The maximum height of the SE used is 96
m for consistency with Case Studies 2 and 3. Though this
considerable height hardly influences the SE generation for
ordinances of Type 1, it has been chosen to demonstrate
Table 3 Solar radiation simulation parameters
Buildings Ground
Reflectance values 35% 20%
Main radiance parameters –aa .2 –ab 5 –ad 2048 –ar 64
Fig. 5 Determination of the height of the translated grid point for one facade sample (gray square) for the required period (left). Solar
envelope upper surface generated using all the translated grid points for one facade sample for the required period (right)
De Luca and Dogan / Building Simulation
10
the potentialities of the novel method for ordinances of
Types 2 and 3.
For the month/day/hours setting has been taken into
account the period between 10:00 and 14:00 on 21.12. For
the quantitative sun vector selection has been selected
Option 1 since all the 4 hours of duration time are required.
This is also the reason why the qualitative sun vector selection
is not possible for ordinances of Type 1. The time-step used
is 60 (ts60 = 1 minute). Due to the limited total quantity of
hours as the required period it is possible to use a high level
of accuracy of the time input (time-step) without incur in
computationally intensive calculations. Hence for ordinances
of Type 1 it is possible to generate only one type of SE (Fig. 6).
Results are presented in Fig. 7. On 21.12 the percentage
of samples with direct solar access as required by regulation
is 100%. This is evidence that the new method to generate
SEs including the context, that permits to construct the
largest possible SEs fulfilling the requirements, is extremely
reliable reinforcing previous studies (De Luca and Voll 2017).
Being the regulation relative to the day with the least
availability of sun light hours, in the northern hemisphere,
the direct solar access as required by regulation (4 hours per
day between 10:00 and 14:00) is fulfilled for all the samples
also for all the other analyzed periods, 100% for typical hot
week (17–23.08) and cold week (27.01–02.02) and 98.9% for
all year, due to their longer sun light duration per day. The
reductions of the average all day sun light hours per facade
sample comparing the existing situation which ranges from
a high of 99.4% to a low of 81%, and the similar ones for the
total all day sun light hours which ranges from a high of
99.2% to a low of 81.6% show that direct solar access before
and after the required hours is not affected by the SE for the
required period and that it is reduced in different ways
depending on the length of the analysis period and the season.
Average all day incident and total solar radiation reductions
per sample are from 78.3% to 91.6% for the first and from
86.7% to 95.7% for the latter.
Results show that during all year and warm season all
the reductions are similar, whereas during cold periods, the
required day and the typical cold week, total solar radiation
is reduced significantly less. This shows a beneficial effect
of reflected solar radiation on the SE surfaces mostly when
sun altitude angles are small.
4.2 Ordinances of Type 2
For the ordinances of Type 2 the plot is located in an urban
site in Warsaw, Poland (Lat. 52.22° N, Lon. 21.01° E). The
buildings of the urban environment are located at variable
distance from the plot. For this case study samples with size
of 3 m by 3 m are used though the rows used as shadow
fence have been located using a center height of 4.5 m (Fig. 8).
The maximum height of the SE used is 96 m, twice the
maximum height of the existing buildings. This choice was
made to test the variability and flexibility of the new method
to generate SEs with algorithmically selected time-step to
accumulate sun light hours. This selection takes into account
the required minimum of 3 hours between 07:00 and 17:00
for permanently occupied rooms on 21.03 and 21.09. Hence
the analysis period is composed of 20 hours divided in two
groups of 10 with a time-step of 30 (ts30 = 2 minutes). The
larger time-step comparing Case Study 1 has been chosen
due to a larger quantity of hours to be taken into account.
The quantitative selection was set to Option 2 with an input
of a 3 (hours) target. SEs have been generated using all the
5 qualitative selection methods to test the different size and
shapes that can be generated with the new method (Fig. 8).
The largest SEs are generated with Methods 1 and 3 for the
selection of sun vectors with larger sun altitude angles and
the smallest with Methods 2 and 4 for the presence of
surrounding facades facing east and west as discussed in
Section 3.4.2. Method 5 permits to realize a SE with a medium
size characterized by a peak in the center of the plot due to
the selection of sun vectors close the plot corners (Fig. 8).
Results of SE size, method validation and performance
analysis allowed on surrounding facades are presented in
Fig. 9. During the required period the percentage of samples
with the required minimum 3 hours of direct solar access is
an average of 98.1%. The very small discrepancies comparing
the full required minimum 3 hours (100%) of direct solar
access, due to the computational generation of the SE mesh,
show that the proposed method is reliable in generating
Fig. 6 Left - The existing situation urban area used as Case Study 1. Right - The solar envelope generated for the city of Boulder (CO)
De Luca and Dogan / Building Simulation
11
SEs using different procedures that produce very different
massing outcomes. The average all day sun light hours per
sample and the total all day sun light hours present similar
reductions respectively from 82.9% and 81.3% (SE 3) to
98.9% and 99.1% (SE 2). Same trend is for the average all
day incident and total solar radiation reduction per sample
with substantial similarity of the reduction of the two
performances. Results show that in the chosen urban
configuration, differences of reduction of direct solar access
and solar radiation are in a range of maximum 18% whereas
all the SEs guarantee the required direct solar access (Fig. 9).
The other analyzed periods are all year, typical hot week
(13–19.08) and typical cold week (08–14.12). The results
presented in Fig. 9 show that for whole-year and typical hot
Fig. 7 Results of: solar envelope volume (left axis), percentage of samples with direct sun light between 10:00 and 14:00 on 21.12, average
all day sun light hours reduction per sample, total all day sun light hours reduction, average all day incident solar radiation reduction per
sample, average all day total solar radiation reduction per sample (right axis). Required period (10:00–14:00 on 21.12), all year, typical
hot week and typical cold week (The values represent comparison with existing situation)
Fig. 8 The existing situation urban area used as Case Study 2 (upper left). The solar envelopes generated with the 5 methods for the cit
y
of Warsaw
Fig. 9 Results of: solar envelope volume (left axis), percentage of samples with ≥ 3 direct sun light hours between 7:00 and 17:00 on 21.03
and 21.09, average all day sun light hours reduction per sample, total all day sun light hours reduction, average all day incident solar
radiation reduction per sample, average all day total solar radiation reduction per sample (right axis). Required period (7:00–17:00 on
21.03 and 21.09), entire year, typical hot week and typical cold week (The values represent comparison with existing situation)
De Luca and Dogan / Building Simulation
12
week analyses the reduction of direct solar access and solar
radiation for the 5 methods increase comparing the required
period and have similar ratios. During typical cold week
the reduction of percentage of facade samples receiving the
specific direct solar access of the required period increases
(larger reduction) significantly more than the general
reduction of solar access and solar radiation for the entire
day. This is due to the fact that during December and in
urban environment facades facing north, east and west can
receive less than 3 hours of direct solar access per day. The
3 hours requirement during spring and autumn equinox of
the Polish ordinance is penalizing more solar access during
the winter comparing the requirements of the other two
ordinances in relation to winter sun access. Further, Case
Study 2 confirms that for all 5 methods the presence of the
SEs advantage total solar radiation in winter reflecting sun
energy on surrounding facades.
4.3 Ordinances of Type 3
For the ordinances of Type 3 the research investigates a
case study in the city of Tallinn, Estonia (Lat. 59.43° N, Lon.
24.75° E). The urban environment is characterized by
buildings closer the plot and at a more uniform distance
comparing previous case studies. The facade samples 3 m
by 3 m in size generated through the described process are
located using a center height of 4.5 m. Again a height of 96 m
has been chosen to test whether the new method to generate
SEs is efficient and flexible in dense urban environment due
to the hours selection options.
The first selection to take into account is the month/
day/hours. All the hours of each of the 123 days between
22.04 and 22.08 have been selected using a time step of 6
(ts6 = 10 minutes). A larger time-step has been selected
comparing previous case studies due the large quantity of
sun light hours to be taken into account for the period of
123 days, to limit the computation intensive calculations.
Nevertheless, 10 minute time-step is an adequate frequency
to guarantee accurate SE generation. For the quantitative
sun vectors selection Option 3 has been chosen. For the
qualitative the input used is 50 (50% of actual direct solar
access). Consequently, SEs have been generated using all
the 5 methods of qualitative selection to test the different
outcome in terms of size and shape (Fig. 10).
Results of SE size, method validation and performance
analysis allowed on surrounding facades are presented in
Fig. 11. The largest volume SEs are generated with Methods
1, 3 and 5. The smallest SE is generated with Method 2.
The trade-off Method 4 generates a smaller SE than those
generated with the methods to maximize the size with the
scope to guarantee larger incident direct solar radiation.
This shows that the methods that can select firstly the sun
vectors from outside the plot can generate SEs that are
larger than those generated with other methods.
Further, to validate the SEs generated with the 5 different
methods the performance they allow on the surrounding
facades have been analyzed for the 4 periods in relation
to the direct solar access required by the Estonian daylight
standard, general sun light hours and solar radiation
variations.
During the required period the percentages of samples
with the required minimum 50% of direct solar access hours
comparing the existing situation every day between 22.04
and 22.08 are an average of 98.9%. As for previous case
studies, these results support that the new method generates
SEs of diverse morphological character that allow the required
solar access on the surrounding facade. The average all day
sun light hours reductions per sample comparing existing
situation are between 74.3% (SE 3) and 98.7% (SE 2). The
total all day sun light hours reductions are between 72.7%
Fig. 10 The existing situation urban area used as Case Study 3 (upper left). The solar envelopes generated with the 5 methods for the cit
y
of Tallinn
De Luca and Dogan / Building Simulation
13
(SE 3) and 97.3% (SE 2). Similarly, for both average all day
incident and total solar radiation reduction per sample the
least values are for SE 3 and the largest for SE 2. The best
direct solar radiation performance guaranteed by SE 2
confirms the method used to build it. For all the SEs, the
total solar radiation is larger than the incident, the larger
increase being the one of SE 3 from 67.1% to 74.1% due to its
larger reflecting mass (Fig. 11). The other analyzed periods
are all year, typical hot week (01–07.06) and typical cold
week (22–28.12). As presented in Fig. 11, the percentage of
samples with the required minimum 50% is reduced up to
67.8% (SE 1/3/4/5) for all year, up to 99.4% (SE 1/3/5) for
typical hot week and up to 68.6% (SE 1/3/4/5) for typical
cold week for all the 5 methods.
The average all day sun light hour reduction per sample
and the total all day sun light hours reduction are increased
(larger reduction) comparing the required period. The
average all day incident and total solar radiation reduction
per sample also present larger reductions. Results show that
at the northern latitude of Tallinn and for the chosen urban
environment during typical hot week reductions comparing
existing situation are very similar to the period between
22.04 and 22.08 being the month of June in the middle of
the required period. During all year the reduction of the
required 50% is larger than the total amount of sun light
hours. This underlines that the utilization of SEs allows
modelers to ensure that new construction only has a small
impact on existing buildings. During typical cold week results
are opposite due to the fact that samples toward north never
receive direct solar access penalizing more the total than
average or percentage values. Also in the case of Tallinn
total solar radiation is reduced less during all the periods
above all during typical cold week due to closer distances of
the facades from the plot. This is evidence that a meaningful
urban design with buildings located at optimal distances
can increase reflected solar radiation on building facades in
cold climates.
5 Discussion
In this section three aspects of the presented work are
discussed: Firstly, a comparison of the new SE method against
existing methods to validate its potentialities is shown.
Secondly, an analysis of the computational expense and level
of accuracy is demonstrated. Thirdly, a new morphological/
design potential which arises from the strategic utilization
of the new method is discussed.
5.1 Comparison with existing method and tools
To validate the proposed method and tool, SEs have been
generated using the existing method and the proposed
method for all the three types of ordinance and relative
location. Consequently, the volume and direct solar access
allowed on surrounding facade has been calculated and
compared with size and performance of SEs generated with
the proposed method. Results are presented in Table 4 and
Fig. 12.
For ordinances of Type 1 a new urban environment
for the city of Boulder (CO) has been built using building
masses at shorter distance from the plot comparing the one
used for the relative case study. The reason is that, since the
ordinance requires that direct solar access is guaranteed on
surrounding facades from 10:00 to 14:00 during 21.12, being
the sun at its highest positions in the sky, buildings located
far from the plot do not influence the shape of the SE even
Fig. 11 Results of: solar envelope volume (left axis), percentage of samples with ≥ 50% of actual direct sun light hours, average all da
y
sun light hours reduction per sample, total all day sun light hours reduction, average all day incident solar radiation reduction per
sample, average all day total solar radiation reduction per sample (right axis). Required period (all day from 22.04 to 22.08), entire year,
typical hot week and typical cold week (The values represent comparison with existing situation)
De Luca and Dogan / Building Simulation
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Table 4 Comparison of volumes (V) and direct solar access
performance calculated as facade samples fulfilling the requirement
(sf) for SEs generated with existing and proposed method
Ordinance Method V (m3 × 1000) sf (%)
Existing 198 100
1
Boulder (CO) Proposed 219.5 100
Existing (07:00–10:00) 262.4 91.4
Existing (11:00–14:00) 621.2 68.1
Existing (14:00–17:00) 163.2 94.8
2
War s a w
Proposed #3 368.6 95.7
Existing (06:00–14:00) 160.1 100
Existing (09:00–17:00) 387.5 97.4
Existing (13:00–21:00) 38.2 100
3
Tallinn
Proposed #3 564.7 98.7
if using the developed method which takes the context into
account. The test performed shows that the proposed method
permits to generate a larger SE (Fig. 12-1b) comparing the
existing method (Fig. 12-1a) for the capability to include the
context in the calculations. Both the SEs generated with the
existing and proposed method guarantee 100% of required
solar access on surrounding facades. Nevertheless, the small
difference of volume shows that, as anticipated, the existing
method is still a valid option for ordinances that require a
fixed start-and-end hour time input (Type 1) above all for
scattered urban environments, whereas it presents significant
limitations for ordinances of Types 2 and 3.
For ordinances of Type 2 the same urban environment
located in the city of Warsaw of Case Study 2 has been used.
The solar access regulation requires that 3 hours of direct
sun light should be guaranteed during 21.03 and 21.09
between 07:00 and 17:00. The main limitation of the existing
method is that it requires to define the start-and-end hour
time input for the 3 hours, but the designer doesn’t know if
and when the 3 hours of sun light are available on each
facade and portion of it. For the present test 3 periods of
3 hours have been used inside the timeframe between 07:00
and 17:00: 07:00–10:00, 11:00–14:00 and 14:00–17:00. For
comparison has been used the generated SE with proposed
Method 3. Results presented in Table 4 show how the SEs
generated with the existing tools are miscalculated and poorly
performative. They are smaller allowing smaller percentage
of surrounding facade samples fulfilling the requirement or
the one which is way larger allows for significantly smaller
required solar access comparing the one generated with the
proposed method (Figs. 12-2a and 12-2b), which permit to
build the maximum possible volume allowing the required
direct solar access (the small delta from 100% being due to
SE grid density as discussed in next subsection).
For ordinances of Type 3 has been used the same
surrounding buildings layout in the city of Tallinn as for
Case Study 3 and the Estonian standard which requires that
existing premises receive at least 50% of sun light hours
every day between 22.04 and 22.08 comparing the existing
situation. During these days, the shortest of the period, direct
sun light is available approximately for 15 hours between
06:00 and 21:00. For the generation of SEs using the fixed
start-and-end hour time input of the existing method,
3 periods of 8 hours (approximately the half of 15 hours)
have been used for each day of the required period:
06:00-14:00, 09:00-17:00 and 13:00-21:00. Results presented
in Table 4 show that all the tested SEs allow the required
solar access (considering the delta from 100% due to SE
grid accuracy settings), nonetheless the one generated with
the proposed method is way larger than those realized with
the existing method as also shown in Figs. 12-3a and 12-3b.
Tests showed that the proposed method can generate
Fig. 12 Solar envelopes generated with the existing method (upper row) and proposed method (lower row) for ordinance of Type 1 Case
Study Boulder (CO) (left column), Type 2 Case Study Warsaw (middle column) for hours 14:00–17:00 (2a) and method 3 (2b), and Type 3
Case Study Tallinn (right column) for hours 09:00–17:00 (3a) and method 3 (3b)
De Luca and Dogan / Building Simulation
15
SEs with the maximum possible volume in order to guarantee
required solar access on surrounding facades and additionally
allows the possibility to choose between different morphological
output and performance.
5.2 Computation time and solar envelope accuracy
Tests have been conducted to assess variation of performance
of solar envelopes on the basis of different level of accuracy
and computation time needed to realize them. The two
factors influencing SE accuracy, i.e. volume and level of detail,
which is responsible of the quantity of required direct solar
access received by surrounding facades, and computation
time, are the time-step (subdivision of sun light hours) and
the plot subdivision grid size, i.e. distance between grid points,
which generate the SE mesh. The computer used for the
work and tests has a single processor Intel Core i7-4800MQ
2.70GHz and 16 Gb of RAM.
For the tests, the SE of Case Study 2 (Warsaw), realized
with Method 1 (larger sun vertical angle) using a time-step
of 2 minutes (ts30) and a distance between grid points of
4.5 m for the square plot with 90 m side, has been used as
base case. Additional generations of the same SE have been
processed in two ways: keeping fixed the 4.5 m gird points
distance and using different time-steps of 1, 5, 10, 15, 30 and
60 minutes (respectively ts60, ts12, ts6, ts4, ts2 and ts1);
using a fixed time-step of 1 minute (ts60) and using different
grid points distance of 1.5 m, 3 m, 4.5 m, 7.5 m, 10.5 m,
16.5 m and 28.5 m (for increments of 1.5 m, 3 m, 6 m and
12 m). The quantity of required direct solar access on
surrounding facades has been computed as the percentage
of facade samples fulfilling the requirement. Results are
presented in Table 5.
The reduction of temporal resolution (smaller time-step)
decreases of a small fraction computation time and percentage
of facade samples fulfilling the requirement, due to an
increased SE volume, until ts2. Using only one vector for
each sun light hour (ts1) computation time is not reduced
significantly, whereas SE performance is, due to a further
increase of its volume. For Case Study 2 of the present work
ts30 has been used because guarantees the higher percentage
of samples fulfilling the requirement (95.7%) the same as
ts60 but in a smaller computation time.
Results show that variation of plot grid points distance
influences computation time at a greater extent without
compromising significantly solar access performance. Using
a refined mesh with points at 1.5 m distance it is possible
to obtain a level of accuracy of SE to achieve 100% of
surrounding facade samples fulfilling the requirement, at
the expenses of very long computation time. It is interesting
to notice that grid size of 10.5 m produces a SE which
guarantees same level of direct solar access on surrounding
facades as grid size 3 m which is 11 times slower. A further
result shows that that the volume of the SE doesn’t change
linearly when increasing the distance between grid points
and relative decrease of computation time.
Nevertheless, it is important to underline that such
performance variations depend largely on the type of
ordinance, SE generation method among the proposed ones,
and urban morphology surrounding the plot. Using similar
computer characteristics as those mentioned and software
as for the present study, it is advised to use the highest time
accuracy possible for a quantity of sun vectors not exceeding
1000 to keep the simulation time below 1 hour.
The method developed and future computer tool permits
the designer to control the two factors to choose between
computational speed and accuracy of results or trade-offs
between the two. The proposed method has been developed
using Grasshopper and environmental design plug-in realized
in Python, either presenting the downside of slow com-
putation speed. The tool under development by the authors
will be realized in C# for increased computation speed.
Table 5 Values used for parameters of time-step (ts) and grid points distance (g) for assessment of computation time (t) and SE accuracy
through its volume (V) and facade samples fulfilling the requirement (sf). In thicker borders box the values used for Case Study 2
Solar envelope generated with fixed plot grid points distance 4.5 m
ts 60 30 12 6 4 2 1
t (h:m:s) 00:27:00 00:24:33 00:23:44 00:23:19 00:23:17 00:23:30 00:23:13
V (m3 ×1000) 340.4 341.8 347.1 349.4 374.3 378.2 393.0
sf (%) 95.7 95.7 94.8 94.8 93.1 93.1 88.8
Solar envelope generated with fixed time-step 1 minute (ts60)
g (m) 1.5 3 4.5 7.5 10.5 16.5 28.5
t (h:m:s) 06:54:50 00:54:17 00:27:00 00:10:23 00:07:07 00:05:14 00:04:17
V (m3 ×1000) 339.6 339.7 340.4 339.8 337.8 334.4 346.3
sf (%) 100 95.7 95.7 95.7 95.7 94.8 89.7
De Luca and Dogan / Building Simulation
16
5.3 New morphological potentiality
The 3 case studies show that for ordinances of Types 2 and
3 the novel method can generate different SEs for size and
shape on plots located in similar urban environments for
the same ordinance, whereas it is possible to generate only
1 shape and size SE for ordinances of Type 1. All the SEs
generated fulfill the requirements given in solar ordinances
for the neighboring building facades.
The SE generated for ordinances of Type 1 has a regular
shape resembling a truncated wedge with one main sloped
surface toward the south facing facades that are the most
affected by the required direct solar access time frame from
10:00 to 14:00 (Fig. 6). A building located in the plot that
must be contained into the SE to not overshadow the
surrounding buildings when it is not allowed, will be taller
if located toward the southern edge of the plot and smaller
if located toward the northern edge of the plot. Every option
about the location of the new building will lead to a building
contained into the SE.
The SEs generated for ordinances of Types 2 and 3 have
different shapes as the algorithm permits the designer to
select sun light hours/time steps within the analysis/prescribed
period. The shapes are more or less articulated resembling
sea weaves and mountain peaks for Case Study 2 or multi-
sloped roofs and thick extrusions for Case Study 3 (Figs. 8
and 10). Some of these SEs, SE 3 for Case Study 2 and above
all SE 3 and SE 5 for Case Study 3 have a flat surface on the
top. Since the SEs have been generated using a considerable
maximum height, this characteristic means that if a new
building to be constructed on the plot is located in
correspondence of the flat surface its height is not bound
anymore to the SE volume.
To test this finding a building 144 m in height, 1.5 times
the maximum height used to generate the SEs, has been
located in the plot and urban area of Case Study 3 with its
footprint not exceeding the projection on the ground of the
flat surface on the top of SE 3 (Fig. 13). The sun light hours
analysis on the surrounding facade samples show that this
massive and tall building guarantees the required minimum
50% of direct solar access per sample comparing the existing
situation every day of the period between 22.04 and 22.08
as stated by the direct solar access of the Estonian daylight
standard. The test has been done using not only the single
row facade samples used to generate the SE but all the
samples of the facades facing the plot. In this way it has
been possible to test the reliability of the method as well for
the single row of samples used as shadow fences. The result
of minimum 65% of direct solar access per sample on the
surrounding facades confirms the reliability of the method
and the discussed finding (Fig. 13).
The possibility to generate SEs selecting firstly sun
vectors from outside the plot and secondly those that travel
through the plot and in addition the possibility to select
sun vectors with larger sun altitude or close the plot corners
among those passing through the plot, given by the qualitative
selection Methods 3 and 5, thus permit, depending on the
urban environment, to find areas of the plot where the
height of the building is not limited anymore by the SE.
6 Conclusions
The present paper introduces and discusses a new method
to generate solar envelopes in urban environments to be
used in urban design processes by architects and planners
to determine the maximum size that new buildings cannot
exceed to guarantee the required direct solar access on existing
surrounding facades. The research overcomes significant
limitations in existing tools to ensure compatibility with
the majority of solar ordinances globally.
Direct solar access on existing facades ordinances are of
3 types that require for every day: (1) exact hours timeframe;
(2) quantity of hours; (3) percentage of actual direct solar
access hours. The existing SE design tools can be used only
for ordinances of Type 1 and in low density urbanization
areas. The proposed method permits to efficiently generate
SEs for dense urban areas and for ordinances of Types 2
and 3, and in addition also of Type 1, permitting the
Fig. 13 Left - Solar envelope for Case Study 3 generated with method 3 and building massing exceeding its volume. Right - Direct solar
access hours analysis and calculation of percentage of sun light hours per sample allowed by the building of 144 m of height in
comparison with the existing situation (minimum required 50%)
De Luca and Dogan / Building Simulation
17
unprecedented selection of the required sun light hours by
the designer.
The generated SEs are the largest possible to respect
rights of light and fulfil the requirements on surrounding
facades than those obtained with conventional tools because
context is taken into account, efficient because they allow
the exact direct solar access hours quantity as required by
the specific ordinance, and flexible because the designer can
chose between different shape and size of SEs that allow
different quantity and quality of natural light on neighboring
facades but all guaranteeing the required sun light hours.
This potentiality gives designers also the opportunity to
integrate form studies and direct solar access performance
analysis in urban environments.
The proposed method is intended to help architects
and planners as well as developers and municipalities to
efficiently and easily determine the correct size and different
possible massing distribution of new buildings that guarantee
direct solar access on surrounding facades in urban areas to
improve the quality of the built environment.
Future work of this research is the development of a set
of computer tools, already in progress, to be included in
environmental design software popular among architects
and planners. The tool will be a free plug-in for the
parametric and generative design software Grasshopper for
Rhinoceros. The research will be further developed to
include different types of analysis together with the direct
solar access one, such as pedestrian comfort, daylight and
energy to evaluate different impacts of building masses
determined by solar envelopes on the urban environment.
The scope is to facilitate the design of sustainable, integrated
and efficient cities characterized by livable and walkable
open spaces and comfortable buildings.
Acknowledgements
The research has been supported by the Estonian Centre
of Excellence in Zero Energy and Resource Efficient Smart
Buildings and Districts, ZEBE, grant 2014-2020.4.01.15-0016
funded by the European Regional Development Fund.
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