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A Novel Multi-Criteria Method for Building Massing Based
on Energy Performance and Solar Access
The Mixed Solar Envelope (MSE) method
Abel Sepúlveda1, Francesco De Luca1
1Department of Civil Engineering and Architecture, Tallinn University of Technology
1{absepu|francesco.deluca}@taltech.ee
This paper proposes a novel multi-criteria method for building massing based on energy
performance and solar access allowed to the surrounding buildings (Mixed Solar
Envelope (MSE) method). We used a single thermal zone simulation-based methodology
to validate the method. We applied the MSE method in a generic urban zone located in
Tallinn, Estonia. Determining the building form, the designer can prioritize energy
performance and/or solar access for each studied neighbor’s room, as well as the
importance between studied rooms. The method allowed to generate building masses
(MSEs) capable of saving up to 73% and 67% of the total annual energy consumption in
office and residential rooms with window-to-wall-ratio of 80%. As a tool to negotiate
between different rooms, the total annual energy savings was between 56-80% when
considering a pure energy-based criterion. The annual energy savings was between 26-
30% while maximizing the annual number of sun hours when considering solar access-
based criteria.
Keywords: Energy Efficiency, Solar Access, Building Massing, Reverse Solar Envelope,
Solar Envelope, Multi-Criteria Design, Early Design Stages, Multi-Optimization.
INTRODUCTION
Predictions say that the 80% of the world population
will live in urban environments by 2030 (Sanaieian et
al., 2014). The design of nearly Energy Zero Buildings
(N ZEB) wil l be key to im prove tenants’ economy level
and decreasing the world warming effect. In
addition, visual comfort, specifically solar access (SA)
has been proved essential to maintain good levels of
human health and mental performance (Samuels,
1990; Lockley, 2009). Nowadays, architects often
have to face challenges during early design stages
when trying to reach a good balance between strict
energy performance requirements and SA levels not
only for the new but the surrounding buildings.
One of the most relevant decisions during early
design stages is the building massing. There are
many investigations that proposed efficient
methods to generate building massing on a
buildable plot based on the well-known concept of
the solar envelope (SE), which represents the
maximum buildable volume on a plot (Knowles,
1980). Several aspects could be taken into account
when massing a new building such as the
surrounding buildings (Capeluto and Plotnikov,
2017; De Luca, Nejur and Dogan, 2018), different
solar ordinances (De Luca and Dogan, 2019) and
methods to consider the quality and quantity of the
daily sun hours (Sepúlveda and De luca, 2020). In
practice, due to the non-mandatory nature of
daylight standards in most countries, the designer
Volume 1 – Co-creating the Future – eCAADe 40 | 649
would have flexibility to define a building massing
even if the volume of the new building does not
guarantee the same SA level for all the surrounding
buildings. Indeed, the recently developed method
called Reverse Solar Envelope allows the
consideration of a certain maximum obstruction
index (OI) for each cell of the theoretical block
(generated by the extrusion of the buildable plot to
a maximum buildable height) (De Luca, Dogan and
Sepúlveda, 2021). Moreover, energy performance
and solar radiation have been considered as
objectives in previous studies developed through
focused on multi-objective optimization (Wang,
Song and Tang, 2020; Natanian and Wortmann,
2021; Xia and Li, 2021). The majority of these
methods are based on energy simulations, often
requiring long times and difficult to conduct by non-
expert designers. Thus, the learning curve of these
energy-simulation based methods could be an
important user barrier in practice (Nault et al., 2018).
Other studies proposed methods that help
architects and designers to generate external voxel-
based shading systems to improve the energy
efficiency of existing rooms (Sargent, Niemasz and
Reinhart, 2011). Designers, architects, and engineers
are encouraged to consider heating and cooling
passive strategies in cold climate countries such as
Estonia (De Luca, Dogan and Kurnitski, 2018), where
the current energy performance NZEB requirements
are even stricter than those recommended in the
well-know standards such as LEED or BREEAM
(Seinre, Kurnitski and Voll, 2014).
NOVELTY AND AIMS OF THIS RESEARCH
Although, there are several building massing
methods that take into account the solar access of
both, existing and new buildings (Capeluto and
Shaviv, 2001; De Luca and Dogan, 2019; De Luca,
Dogan and Sepúlveda, 2021). There is a lack of
building massing methods based on simultaneously
energy performance and solar access of the
surrounding buildings that could be used as a
negotiation tool by designers without the need of
time-consuming energy simulations. There is a need
for easy-to use methods for building massing that
help architects to design new buildings that improve
the annual energy performance of the surrounding
buildings (through heating and cooling passive
strategies) while maintaining adequate solar access
levels or to find the best trade-offs between energy
consumption and solar access. Consequently, the
aims of this paper are the following:
• To propose a multi-criteria method for building
massing based on beam solar radiation and solar
access of the surrounding buildings (MSE) that
can be adapted to different climates;
• To study how building masses generated
according to beam solar radiation during
winter/summer hours defined by the Estonian
overheating regulation can affect the annual
energy consumption (heating and cooling);
• To validate MSE method as a negotiation tool
that could be used for designers to balance
energy efficiency and solar access of the
surrounding buildings during early design
stages.
METHODOLOGY
In this section, the performance variables considered
in our method are presented and justified. Finally,
the calculation of the fitness value for each cell
influenced for each combination of windows/rooms
is described. We used a single-zone simulation-
based methodology to validate the MSE method.
Specifically, the energy simulations were conducted
with the validated software EnergyPlus (U.S.
Department of Energy, 2015). The solar access
assessment was done with the Grasshopper plug-in
for Rhinoceros Solar Envelope Tools (Sepúlveda and
De Luca, 2022).
Building on existing studies (Kaftan and Marsh,
2005; Sargent, Niemasz and Reinhart, 2011) which
proposed external voxel-based shading systems to
improve the energy efficiency of buildings, the
present work proposes a negotiation tool usable
during early design stages. The main idea of MSE is
to evaluate how important is each cell of the
650 | eCAADe 40 – Volume 1 – Co-creating the Future
theoretical block for energy use and solar access of
the surrounding room studied. Finally, the designer
could filter the cells whose fitness value (F) is above
a chosen threshold, which varies between 0 and 1)
(e.g. with a Fratio=0.5 the designer is selecting all the
cells whose F value correspond to the mean F value).
The critical aspect is that energy and solar access are
often in conflict. On one hand, as defined in the RSE
method, we considered the OI of a cell i as the
number of time steps (e.g. each hour) during a
specific analysis period (e.g. the whole year) that the
cell i is blocking the sun. On the other hand, we
considered the incident beam solar radiation related
to each window as a representative factor of solar
heat gains, and consequently of the annual cooling
and heating energy consumption. Although,
shading factors (ratio of the glazing area that is in
shadow) depend on multiple components of the
solar radiation (e.g. diffuse, reflected, direct, etc.)
(Tamm et al., 2020), we only considered the beam
component has main factor related to the energy
performance (Antretter, 2016). By doing this
simplification, our method does not have to depend
on energy simulations, thus being easier-to use.
The steps of our proposed method are shown in
Figure 1: incident beam solar radiation calculation
(step 1), mesh cells and OIs calculation (step 2),
shading factors and net energy fitness values
calculation using (1), (2) and (3) (step 3), fitness
values (Fs) calculation (4) for a certain criterion (step
4), and selection of the cells whose F value is above a
chosen threshold (Fratio) (step 5).
𝐹,∑𝛿𝛼𝐹𝑛,𝛽
1,
,
(4)
Where:
- SRw,k is the incident solar radiation associated to
the window w at the hour k;
- maxSRw is the maximum hourly incident solar
radiation associated to the window w;
- SFi,k is the shading factor associated to the mesh
cell i at the hour k;
- Fhi,w/Fci,w is the passive/heating and cooling
fitness value (between 0 and 1) associated to the
cell i at the hour k;
- Fni,w is the net energy fitness value (between -1
and 1) associated to the mesh cell i at the hour k;
- αw and βw are the weight factors for energy and
solar access, respectively (αw+ βw=1);
- 𝛿 is the weight factor (between 0 and 1)
associated to the window w (∑𝛿
1);
- Nv,w is the number of visible sun hours from the
window w;
- Nw is the number of windows/rooms studied;
- Nh and Nc are the number of winter and summer
hours, respectively.
Figure 1
General workflow
proposed in this
research.
𝐹ℎ,∑,/,
,
(1)
𝐹𝑐,∑,/,
,
(2)
𝐹𝑛,𝐹𝑐
, 𝐹ℎ,
(3)
Volume 1 – Co-creating the Future – eCAADe 40 | 651
Case studies
For the case studies, we considered a generic urban
environment located in Tallinn, Estonia (Lat. 59.43◦
N, Lon. 24.75◦ E) with different room combinations
surrounding the building mass under investigation.
Tallinn, capital of Estonia, is located at the north
coast of the country. Tallinn has a warm summer
humid continental climate (Dfb) according to
Köppen-Geiger classification (Climate onebuilding,
2022). The average annual temperature is +6.4°C and
the average temperature during the warm season is
+16.2°C (Estonian Weather Service, 2021).
Element
Construction
Thermal
transmittance
(W/(m2K))
External wall Conc. 150 mm
EP 280 mm
Conc. 50 mm
0.128
Floor slabs,
internal walls
Conc. 250 mm 3.59
Window
frame
Aluminum
50 mm
0.5
Parameter Residential Office
People density 0.0353 p/m2 0.0588 p/m2
Metabolic rate 1.2 MET 1.2 MET
Eq.| Li.| Pe. PD 3|8|3
W/m2
12|12|5
W/m2
H|C set point 21|27 °C 21|25 °C
Min. Fresh air per
person
14.15 L/s/p 14.15 L/s/p
Min. Fresh air per
area
0.5 L/s/ m2 2.0 L/s/ m2
Occupancy Always 7:00-18:00
(weekdays)
In case study 1, we analyzed the influence of the
MSEs in terms of annual energy consumption
regarding two room types (residential and office),
three orientations (east, south, and west), three
room areas (S: 12.25 m2, M: 24.75 m2, and L: 48.75 m2),
and two WWR values (40% and 80%) (Figure 2). In
case study 2, we showed how to use the proposed
method as multi-criteria negotiation tools for early
design stages in a residential urban area, taking into
account both energy and solar access performances.
The main aim of case study 1 is to study the
potential of our proposed method to improve the
energy performance of the surrounding buildings,
using test rooms. The chosen metric for the case
study 1 is the relative deviation of the total energy
consumption considered (cooling and heating). We
used the validated Energy Plus software to calculate
energy consumption values for all the analyzed
rooms (Figure 2).
Thermal properties of construction materials
and HVAC parameters for Estonian residential/office
rooms are shown in Table 1 and Table 2, respectively
(Estonian Government, 2018). Exterior and interior
emissivity of the opaque surfaces was set to 0.9. We
considered a cost-optimal glazing system: window
triple-glazing system (CalumenLive, 2021) with
thermal transmittance of 0.5 (W/(m2K)), g-value of
0.37 (-), and visual/solar transmittance of 0.63/0.27 (-
) (Sepúlveda et al., 2020; Sepúlveda, De Luca and
Kurnitski, 2022). The efficiency of the heat recovery
temperature was set to 80%. In addition, usage rate
schedules were considered for internal gains (Figure
3) (Estonian Government, 2012, 2018). We
considered the warm period (with potential cooling
need) from April 22 to August 22 according to
Estonian overheating regulation. The consideration
of infiltration is mandatory according to the Estonian
regulations. The infiltration airflow rate (qi) is
calculated using (5) (when the exhaust and supply air
flow rate are the same):
Figure 2
Combination of test
rooms considered
in this study.
Table 1
Thermal properties
of construction
materials.
Conc.=concrete,
EP=Expanded
polystyrene.
Table 2
HVAC parameters
according to
Estonian
regulations.
PD=power density,
Eq.=equipment,
Pe.=people,
H=heating,
C=cooling, and
Li.=lighting
(Estonian
Government, 2018).
𝑞𝑖
. 𝐴
(5)
652 | eCAADe 40 – Volume 1 – Co-creating the Future
Where A is the area of the building envelope in
m2, q50 is the average air leakage rate of the building
envelope that was set to 3 m3/(h⋅m2) according to
the same regulation, and x is the building factor set
to 15 because the height of the surrounding
buildings (Estonian Government, 2018).
RESULTS AND DISCUSSION
This section contains all the results obtained by
applying the general workflow presented in section
“Methodology”. Specifically, the proposed MSE
method was applied in two case studies. Case study
1 consists of analyzing the influence of energy-based
MSEs on different single residential and office rooms’
heating and cooling energy consumption. Thus, case
study 1 is useful to validate two considerations:
beam solar radiation and the static winter/summer
periods used in this study. Case study 2 consists of
using the RSE method as a negotiation tool for
building massing during early design stages in a
residential urban area, considering different energy
and solar access criteria for different room studies.
Case study 1: energy-based
criterion for residential/office rooms
In Figure 4, the annual energy consumption of cases
with and without MSE is displayed. These MSEs were
generated considering a pure energy-based
criterion (α=1, β=0) for each room combination. For
residential rooms with WWR of 80% (Figure 4a), the
total energy savings are between 1% and 67%. The
annual heating consumption decreases when
increasing the room width due to the higher solar
gains caused by larger glazed area. This significant
difference can be due to the low cooling need
related to an east-oriented room of 12.25 m2 (20
kWh/y·m2) in comparison to the high cooling need
related to a south-oriented room of 48.75 m2 (10
kWh/y·m2). In fact, for residential rooms with WWR of
40% (any studied orientation) (Figure 4c), the
presence of a MSE does not help to save total energy
(increments from 8% to 14%). Our method to
generate the MSEs is based on beam solar radiation,
which considers only the direct component of the
solar radiation. In reality, the MSE, as shading
volume, would block not only beam but diffuse and
reflected solar radiation, decreasing the cooling
consumption and increasing the heating
consumption (Tamm et al., 2020). Therefore, when
the cooling need (for any of the studied orientations)
is not significant (nearly null) because for instance, to
a facade with low WWR (40%), the net effect of the
MSE in terms of energy is not desirable, meaning that
the MSE does not have potential to save energy of
the surrounding rooms. However, this increment
would be still lower than the associated to the whole
theoretical block.
For office rooms with WWR of 80% (Figure 4b), the
total energy savings are much larger than those
related to residential rooms: between 33% and 73%.
This significant difference is due to the higher
internal heat gains related to office use (Table 2).
Moreover, for office rooms with WWR of 40%, the
presence of a MSE might help to save total annual
energy: annual energy savings of 3-24%, 1-5%, and
3-14% for rooms facing south, east, and west,
respectively. Indeed, the annual cooling
consumption values are between 0.61 and 1.76
kWh/y·m2 (Figure 4b), giving the MSE the
opportunity to block undesirable sun rays that
would increase the cooling consumption during the
warm season. In this case study located in Tallinn,
Estonia, the consideration of a static summer and
winter periods can be considered a valid assumption
for office rooms with WWR values (higher than 40%).
However, despite the MSE does not seem to help
decreasing the total annual energy consumption for
Figure 3
Usage profiles of
occupancy,
lighting, and
equipment for
residential and
office test rooms
(Estonian
Government, 2018).
Volume 1 – Co-creating the Future – eCAADe 40 | 653
residential rooms with low WWR values, MSEs leaded
to high-energy savings when WWR values of 80%.
Case study 2: considering
trade-off criteria for residential rooms
The previous case study considered different
individual room combinations to evaluate the
influence of the MSEs on the maximum annual
energy savings. In reality, we could consider different
room studies (three 4.5x5.5 m residential rooms with
WWR of 80%) in the same urban environment and be
able to balance different performances for each
room study. To prove that our method could be used
as a negotiation tool, different criteria have been
considered to generate the MSE on the buildable
plot (γw=1/3 = the three rooms have the same
importance to evaluate each Fitness cell value (4)).
Finally, the effect of each MSE in terms of energy
consumption and solar access levels is analyzed.
Criterion C1 is based purely on energy
performance, this criterion is adequate when the
designer prioritizes the energy performance above
solar access of the surrounding rooms (α=1 and β=0
for all the rooms). Criterion C2 is based on a trade-off
between energy performance and solar access for all
the rooms (α=0.5 and β=0.5). Criterion C3 is based on
special needs for each room study, due to the large
cooling need of south oriented rooms, α and β could
be 1 and 0 (energy-based criterion). On the other
hand, residents of east and west oriented rooms
might prefer to keep a reasonable level of solar
access, hence; α and β could be 0 and 1.
The MSEs related to each design criterion (C1,
C2, and C3) are displayed in Figure 6. Fratio is the
threshold value for the final selection of the MSE
cells. A Fratio of 0 and 1 is related to minimum and
maximum F value, respectively. The selection of Fratio
is up to the designer, the higher, the better
performance and less volume the MSE would have.
In this case study, each MSE was generated by
selecting the maximum Fratio to have a voxel-volume
that ensure a continuous connection between the
buildable plot level to the maximum height of 60 m.
In summary, the annual total energy savings and
annual sun hours reduction for different rooms and
design criteria are shown in Figure 5. Moreover, it
can be seen that the pure energy-based MSE (Figure
6) contains higher volume than criteria based on
solar access
Considering C1 (Figure 6a), the buildable
volume is 101196 m3, achieving a total annual
Figure 4
Annual energy
consumption of the
baseline cases and the
influence of Mixed
Solar Envelopes
(MSEs) in terms of
relative annual energy
deviation (cooling and
heating). Residential
rooms with window-
to-wall ratios (WWRs)
of 80% (a) and 40% (c).
Office rooms with
WWRs of 80% (b) and
40% (d).
654 | eCAADe 40 – Volume 1 – Co-creating the Future
energy savings for the residential rooms facing east,
south, west of 52%, 40%, and 36%, respectively.
However, this MSE (Fratio of 0.24) would decrease the
annual sun hours by 80%, 63%, and 56%, for east,
south, and west oriented rooms, respectively. This
difference between energy and solar access
performance was expected since we set α to 1 and β
t0 0 for all the rooms.
Considering C2 (Figure 6b), the buildable
volume is 70956 m3, achieving a total annual energy
savings for the residential rooms facing east, south,
west of 26%, 53%, 30%, respectively. In addition, this
MSE (Fratio of 0.91) would decrease the annual sun
hours by 0%, 35%, 6%, for east, south, and west
oriented rooms, respectively. The decrease of energy
performance of the rooms was expected, since this
design criterion is based on a trade-off between
energy performance and solar access (α=0.5 and
β=0.5 for all the rooms).
Considering C3 (Figure 6c), the buildable volume
is 84240 m3, achieving a total annual energy savings
for the residential rooms facing east, south, west of
26%, 41%, 32%, respectively. In addition, this MSE
(Fratio of 0.9) would decrease the annual sun hours by
2%, 65%, 2%, for east, south, and west oriented
rooms, respectively. The improvement, for one side
of solar access levels for east and west oriented
rooms and on the other hand, the energy
performance for the south-oriented room was
expected since this design criterion priories the solar
access for east/west oriented rooms (α=0 and β=1)
and energy performance for the south oriented
room solar access (α=1 and β=0).
In case of considering, large number of windows
with the same relative importance (constant 𝛿), the
MSE could appear like to the typical SE the stronger
SA-based (𝛽𝑤 closer to 1) is the design criterion.
However, the MSE could appear not necessarily like
the typical solar envelope because the shape of the
MSE would depend on weight factor associated to
each window (𝛿) as well as the relative weight
between energy efficiency (αw) and solar access (𝛽𝑤)
and the Fratio set by the designer. Thus, the MSE
method provides more flexibility to the designer in
early design stages than previous building massing
methods such as the SE and RSE.
CONCLUSIONS
This paper proposes the Mixed Solar Envelope (MSE)
method: a novel multi-criteria method for building
massing based on energy performance and solar
access. We use a single thermal zone simulation-
based methodology to validate our method. The
workflow is implemented as Grasshopper plug-ins
for Rhinoceros. We apply the MSE in a generic urban
zone located in Tallinn. The main outcomes of this
research are the following:
• It was possible to propose a 5-step building
massing multi-criteria method based on beam
solar radiation and solar access. The designer can
prioritize energy performance and/or solar
access for each studied neighbor’s room, as well
as the priority between studied rooms;
• The use of our proposed method would be
specially useful if cooling energy is used for the
room, which would depend on the building
type. Thus, by using the proposed method, it
was possible to generate building masses (MSEs)
capable of saving up to 73% and 67% of the total
energy consumption in office and residential
rooms with window-to-wall-ratios (WWRs) of
80%, respectively;
Figure 5
Annual total energy
savings (%) (a) and
reduction of annual
sun hours (%) of
different residential
rooms studied
when considering
different design
criteria: case A (α=1,
β=0), case B (α=0.5,
β=0.5), and case C
(for East and west-
oriented rooms:
α=0, β=0.5; for
south-oriented
room: α=1, β=0).
γ=1/3 (same
importance for all
windows).
Fratio= 0 is related to
minimum F value
and Fratio= 1 is
related to the
maximum F value.
Volume 1 – Co-creating the Future – eCAADe 40 | 655
• Our MSE method could be used as a negotiation
tool during early design stages to balance
energy performance and solar access a
residential urban area studied. By considering
pure energy-based criterion, total annual energy
savings could be between 56-80%. By
considering solar access-based criteria, total
annual energy savings could be between 26-
30% while maximizing the annual number of sun
hours (reductions up to 6%).
The MSE method was validated for the Estonian
context and a couple of building types. A proper
selection of the heating and cooling schedules is key
for a successful building massing method that could
take into account energy-performance (Sargent,
Niemasz and Reinhart, 2011). Indeed, the used static
schedules defined by Estonian overheating
regulations might not be valid for other climates.
Furthermore, future research should enhance the
MSE method to be used for different latitudes,
building type, WWRs, urban environment, etc.
Additionally, the MSE method will be implemented
as an open source Grasshopper tools to be used by
practitioners during early design stages. Daylight
provision, glare protection, and electric lighting
energy consumption might be included to evaluate
the fitness value of each cell of the theoretical block.
Although the proposed method find relatively fast
building massing options because it does not
depend directly on traditional energy simulations, it
might be necessary to conduct energy analyses to
evaluate how the new building (contained in the
MSE) would affect the surrounding buildings’ energy
efficiency. A future improvement of the MSE method
will be the consideration of proper energy
simulations in order to be applicable to different
climates. Finally, this enhanced MSE method could
be implemented as Grasshopper plug-ins for
Rhinoceros.
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Mixed Solar Envelopes
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656 | eCAADe 40 – Volume 1 – Co-creating the Future
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