An Adaptive Building Skin Concept Resulting from a New Bioinspiration Process: Design, Prototyping, and Characterization

Abstract

Building envelopes can manage light, heat gains or losses, and ventilation and, as such, play a key role in the overall building performance. Research has been focusing on increasing their efficiency by proposing dynamic and adaptive systems, meaning that they evolve to best meet the internal and external varying conditions. Living organisms are relevant examples of adaptability as they have evolved, facing extreme conditions while maintaining stable internal conditions for survival. From a framework based on the inspiration of living envelopes such as animal constructions or biological skins, the concept of an adaptive envelope inspired by the Morpho butterfly was proposed. The system can manage heat, air, and light transfers going through the building and includes adaptive elements with absorption coefficients varying with temperature. This paper presents the developed framework that led to the final concept as well as the concept implementation and assessment. A prototype for heat and light management was built and integrated into a test bench. Measurements were performed to provide a first assessment of the system. In parallel, geometrical parametric models were created to compare multiple configurations in regards to indicators such as air, light, or heat transfers. One of the models provided light projections on the system that were compared with measurements and validated as suitable inputs in grey-box models for the system characterization.

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Citation: Hubert, T.; Dugué, A.;
Vogt Wu, T.; Aujard, F.; Bruneau, D.
An Adaptive Building Skin Concept
Resulting from a New Bioinspiration
Process: Design, Prototyping, and
Characterization. Energies 2022,15,
891. https://doi.org/
10.3390/en15030891
Academic Editors:
Dimitrios Kraniotis and
Katerina Tsikaloudaki
Received: 17 December 2021
Accepted: 18 January 2022
Published: 26 January 2022
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energies
Article
An Adaptive Building Skin Concept Resulting from
a New Bioinspiration Process: Design, Prototyping,
and Characterization
Tessa Hubert 1,2,3,* , Antoine Dugué1, Tingting Vogt Wu 2, Fabienne Aujard 3and Denis Bruneau 4
1NOBATEK/INEF4, National Institute for the Energy Transition in the Construction Sector,
64600 Anglet, France; adugue@nobatek.inef4.com
2
Institute of Mechanical Engineering (I2M), UMR CNRS 5295, Universitéde Bordeaux, 33400 Talence, France;
tingting.vogt-wu@u-bordeaux.fr
3MECADEV UMR CNRS 7179—National Museum of Natural History, 91800 Brunoy, France;
fabienne.aujard@mnhn.fr
4Ecole Nationale Supérieure d’Architecture et Paysage de Bordeaux, 33405 Talence, France;
denis.bruneau@bordeaux.archi.fr
*Correspondence: thubert@nobatek.inef4.com
Abstract:
Building envelopes can manage light, heat gains or losses, and ventilation and, as such,
play a key role in the overall building performance. Research has been focusing on increasing their
efficiency by proposing dynamic and adaptive systems, meaning that they evolve to best meet the
internal and external varying conditions. Living organisms are relevant examples of adaptability
as they have evolved, facing extreme conditions while maintaining stable internal conditions for
survival. From a framework based on the inspiration of living envelopes such as animal constructions
or biological skins, the concept of an adaptive envelope inspired by the Morpho butterfly was
proposed. The system can manage heat, air, and light transfers going through the building and
includes adaptive elements with absorption coefficients varying with temperature. This paper
presents the developed framework that led to the final concept as well as the concept implementation
and assessment. A prototype for heat and light management was built and integrated into a test bench.
Measurements were performed to provide a first assessment of the system. In parallel, geometrical
parametric models were created to compare multiple configurations in regards to indicators such
as air, light, or heat transfers. One of the models provided light projections on the system that
were compared with measurements and validated as suitable inputs in grey-box models for the
system characterization.
Keywords:
bioinspiration; adaptive skin; product design; parametric; regulation factors;
biological models
1. Introduction
Today, challenges in the building sector are mainly focused on reducing energy con-
sumption and greenhouse gas emissions while maintaining indoor environmental quality.
Building designs have gradually evolved with technological advances to comply with
stiffer requirements in terms of comfort, energy, and durability [
1
]. The envelope is more
than a load-bearing component of the building. As it has a major impact on the whole build-
ing energy consumption, it is expected to manage multiple regulation functions between
internal and external environments [2].
New generations of envelopes are emerging: dynamic, auto-reactive, and responsive
envelopes [
3
]; all demonstrate adaptability towards changing environmental conditions
while ensuring comfort and a low carbon footprint. Adaptive envelopes can provide
varying thermal insulation depending on the season, harvest energy, move in accordance
Energies 2022,15, 891. https://doi.org/10.3390/en15030891 https://www.mdpi.com/journal/energies

Energies 2022,15, 891 2 of 19
with the sun’s path, control humidity, and so on, in a way that could help achieve more
sustainable building designs [4].
Mechanisms found in nature reveal inspiring examples of multifunctional envelopes
using very limited local resources [
5
]. Indeed, living species had to evolve under various
environmental constraints, requiring them to develop adaptive and multifunctional fea-
tures. Rising as an innovative approach, bioinspiration in the building field is the topic of
extensive research; it mainly focuses on design processes, frameworks, and tools to ease
the transfer of biological principles into technological responses [
6
–
8
]. Some research has
already led to several adaptive case studies, but very few propose performance assessments
of their design [9].
The current paper presents an adaptive envelope concept derived from a bioinspired
framework. The concept, called Stegos, is a heat-, light-, and air-regulating membrane that
plays the role of a skin placed in front of an opaque wall or a window or acts as an openable
envelope. Stegos was prototyped and tested in real climate conditions. Measurements were
carried out to help with modeling and later to retrieve performance indicators.
2. Adaptive Concept Derived from a Bioinspired Framework
In support of bioinspired processes, a multitude of tools or methods were recently
developed, such as databases, thesauri, ontologies, or taxonomies, for instance [
10
]. Tools
from other disciplines, such as design reasoning theories in engineering [
11
,
12
], can also
facilitate the biomimetic process [
13
] and have already been successfully applied during
design processes [
14
]. However, only a small fraction of patterned bioinspired concepts
or products are commercialized [
15
]. Though this gap is partially due to usual design
constraints (feasibility, strategy, marketing, and so on), it is also mostly related to the
challenges of transferring information from living organisms to technologies [16].
The transferability of an identified biological strategy into technology is complex
without a good understanding of the phenomena at stake in the biological element. Tools to
facilitate interdisciplinarity during bio-inspired design are increasingly numerous,
but they
face limitations as they are frequently designed for and by engineers rather than biolo-
gists [
17
] and often consider a specific objective rather than the full process. The steps of
identification and understanding relevant biological models, and then of transferring a
biological model to a technological concept, would thus deserve more advanced interdisci-
plinarity during the design process.
In the building sector, the practice of bioinspiration has led to multiple bioinspired
buildings designs, but most of them are monofunctional designs, where the inspiring
species demonstrate multifunctional features [
8
]. The assessment of the building per-
formance is often not carried out, which can be seen as a shortcoming [
9
]. In an effort
to tackle these challenges, the authors experimented with a bioinspired framework [
18
]
that they adapted from an ISO standard design process [
19
], with the aim of proposing a
multifunctional design for the building envelope.
2.1. Biological Envelopes as the Starting Point of the Framework
The ISO standard 18458:2015 provides a framework to help harmonize practices in
bioinspiration. Using the biology-push approach, meaning the design process is initiated
by one or several biological solutions [20], we propose a four-step process:
•1: The description of biological models;
•2: The understanding of their principles;
•3: Their abstraction into a concept;
•
4: The validation of its technical feasibility, i.e., the transferability to technology or
solution and its implementation and assessment.
To narrow down the perimeter of the studied biological domain used in step one,
the authors chose to consider living envelopes. Those include the following:

Energies 2022,15, 891 3 of 19
•
Biological envelopes that are the interface of living organisms between their internal
environment and external conditions (for instance, animal envelopes such as skin,
feather, and shells, or vegetal envelopes such as bark);
•
Structures built by animals for shelter, rest, storing, or communication [
21
] (bird nests,
colonies, mounds).
This selection was arbitrarily chosen as species have evolved and developed multi-
functional interfaces through mutations and selective processes, either on their own or
by demonstrating ingenuity and resilience to regulate multiple factors of their internal
environments while facing an environment characterized by varying conditions.
Step two of the applied design process involves selecting a sample of living envelopes
and characterizing their functions in an intelligible structure for building designers. Based
on [
22
,
23
], this approach consists of identifying functions as building envelope criteria
and describing them as the result of environmental disturbances or disruptive actions,
and through
physical phenomena. Disturbances from the environment, whether they
were nonliving elements (climatic conditions such as rain and wind) or living organisms
(metabolism and interaction with other species), were taken into account in the understand-
ing of the biological domain with the support of biologists in adaptive mechanisms [24].
This interdisciplinary work addressed transferability challenges observed in the litera-
ture during step three by providing an understanding of living models at the crossroads of
biology and engineering. Step three is a series of ideation workshops involving various
building sector profiles (engineers, architects, designers) to test this characterization as a
tool of abstraction into multifunctional envelope concepts. The last step (step four) consists
of transposing concepts into technological alternatives and exploring several of them in
their implementation.
The bioinspired concept presented in this article is derived from this framework. We
present in the following how it emerged and was conceptualized, designed, and prototyped.
2.2. Morpho-Butterfly-Inspired Design
The design presented here is based on the Morpho butterfly, one of the selected species
in the sample of biological models. This animal (from the Class Insect and Order Lepidoptera)
is well known for the intense blue of its wings due to the structural properties of scales and
not to pigmentation [
25
]. Table 1presents the structure of the characterization used for the
emerged concept, focusing on two main functionalities: heat and light.
Table 1.
Biotics and abiotic disruptive actions on light, heat, and air regulation functions of the
Morpho butterfly.
Regulation Factor Disruptive Elements Description (Physical
Factor/Features of Wing) Possible Abstractions
Light Butterfly behavior and light
from environment
Iridescence phenomenon from
structural blue color [25]
(reflection/surface texture) Orienting surface elements
towards environment for
optimized heat radiation
Heat
Behavior and radiation from
surrounding environment
Difference in surface properties
between upside and downside
surfaces of wings [26]
(radiation/matter arrangement)
Behavior and air
Forced convection by
shuffling wings [26]
(convection/movement)
Enhancing convection with
moving surfaces or change
in configuration
Air temperature
Increase in emission in near IR
above 50 ◦C [27]
(radiation/matter arrangement
and composition)
Intrinsic emissive properties
adapting to a given temperature
range owing to
structuration surface

Energies 2022,15, 891 4 of 19
To survive, the Morpho requires a body temperature of 36
◦
C [
27
]. Therefore, it has
developed multiple behavioral mechanisms for thermoregulation, such as wing shuffling
to force convection on the thorax or orienting its wings for minimum or maximum solar
radiation. On a morphological level, the chitin-made wings of the Morpho are able to emit
more in the near-infrared when reaching a temperature above a certain threshold so that
they automatically decrease in temperature and return to optimal conditions. Figure 1
shows the illustration of the concept that emerged during the ideation workshop.
Energies 2022, 15, x FOR PEER REVIEW 4 of 18
To survive, the Morpho requires a body temperature of 36 °C [27]. Therefore, it has
developed multiple behavioral mechanisms for thermoregulation, such as wing shuffling
to force convection on the thorax or orienting its wings for minimum or maximum solar
radiation. On a morphological level, the chitin-made wings of the Morpho are able to emit
more in the near-infrared when reaching a temperature above a certain threshold so that
they automatically decrease in temperature and return to optimal conditions. Figure 1
shows the illustration of the concept that emerged during the ideation workshop.
Figure 1. Proposed concept inspired from the Morpho. Credit: Myriame Ali-Oualla and Kaïs Bhouri.
Abstraction from the ideation phase led to a concept of a membrane, both flexible
and ductal, similar to the wings of the Morpho made of chitin polymer. The structure is
a deformable mesh made of identical solid elements held together. When the mesh is
deformed, the elements are pushed away from each other, creating openings between
them. The elements themselves are deployable using flaps that can rotate on a base. The
rotation is induced either by the deformation or by a manually operated device. Addi-
tional functionality is brought by a coating on the flaps, which has an adaptive absorption
coefficient linked to changes in temperature. Table 2 lists the functions managed by this
concept in some of the possible configurations.
Table 2. Managed functions according to configurations. For visual display, flaps are white and
base elements are dark grey.
Mesh Flap Heat Light Air
Flat
Deployed
Adaptive coating less ab-
sorbing with threshold
temperature
+ decrease in temperature
with shadows
Shadows generated by
rotated flaps
Air passing through
if bases are
hollowed
Not deployed Adaptive coating - -
Deformed Deployed
Adaptive coating + de-
crease in temperature with
shadows
Shadows generated by
rotated flaps
Air passing through
the gaps created the
Figure 1.
Proposed concept inspired from the Morpho. Credit: Myriame Ali-Oualla and Kaïs Bhouri.
Abstraction from the ideation phase led to a concept of a membrane, both flexible
and ductal, similar to the wings of the Morpho made of chitin polymer. The structure
is a deformable mesh made of identical solid elements held together. When the mesh is
deformed, the elements are pushed away from each other, creating openings between them.
The elements themselves are deployable using flaps that can rotate on a base.
The rotation
is induced either by the deformation or by a manually operated device. Additional func-
tionality is brought by a coating on the flaps, which has an adaptive absorption coefficient
linked to changes in temperature. Table 2lists the functions managed by this concept in
some of the possible configurations.
The adaptive properties of this concept were chosen to be both auto-reactive (coating,
flaps) and mechanically operated by the building occupants (deformation, flaps).

Energies 2022,15, 891 5 of 19
Table 2.
Managed functions according to configurations. For visual display, flaps are white and base
elements are dark grey.
Mesh Flap Heat Light Air
Flat
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

Table2.Managedfunctionsaccordingtoconfigurations.Forvisualdisplay,flapsarewhiteand
baseelementsaredarkgrey.
MeshFlapHeatLightAir
Flat


Deployed


Adaptivecoatinglessab‐
sorbingwiththreshold
temperature
+decreaseintemperature
withshadows
Shadowsgeneratedby
rotatedflaps
Airpassingthrough
ifbasesarehollowed
NotdeployedAdaptivecoating  ‐ ‐
Deformed


Deployed


Adaptivecoating+de‐
creaseintemperaturewith
shadows
Shadowsgeneratedby
rotatedflaps
Airpassingthrough
thegapscreatedthe
deformationbe‐
tweenelements
Notdeployed‐
Shadowsgeneratedby
rotatedflaps
Theadaptivepropertiesofthisconceptwerechosentobebothauto‐reactive(coat‐
ing,flaps)andmechanicallyoperatedbythebuildingoccupants(deformation,flaps).
2.3.ParametricDesignoftheConcept
Asabiology‐pushapproachwasfollowedforthedesignconcept,noparticular
buildingenveloperequirementsweredefinedasspecificationsforthefinaldesign.How‐
ever,ithadtobemultifunctionalregardingheat,light,andairmanagement.Oncethe
functionswerecharacterized,consideringclearrequirements,aspecificdesigncouldbe
proposed.
Thesefunctionsaresometimesimplementedthroughinterdependentparameters;
asanexplorationbeforeafinalsetofparameters,numerousparametersandtheir
respectivevalueswereproposed(Table3).
Table3.Listofdesignparametersthatwereconsideredfortheconceptandtheirrespectivepossible
values.
ElementsParametersPossibleValues
Mesh
PatternTriangular/radial/squared/fabrics/ropes
MaterialSilicon/rubber/O‐ringjoints/chains
Scaleofdeformation 1cm/10cm/100cm
Typeoftensionforce Point/surfacearea/linear
Numberoftensionforces Single/multiple
Tiltoftension Centimeters/decimeters/meters
Direction Onward/outward
Deployed
Energies2022,15,xFORPEERREVIEW5of19


Table2.Managedfunctionsaccordingtoconfigurations.Forvisualdisplay,flapsarewhiteand
baseelementsaredarkgrey.
MeshFlapHeatLightAir
Flat


Deployed


Adaptivecoatinglessab‐
sorbingwiththreshold
temperature
+decreaseintemperature
withshadows
Shadowsgeneratedby
rotatedflaps
Airpassingthrough
ifbasesarehollowed
NotdeployedAdaptivecoating  ‐ ‐
Deformed


Deployed


Adaptivecoating+de‐
creaseintemperaturewith
shadows
Shadowsgeneratedby
rotatedflaps
Airpassingthrough
thegapscreatedthe
deformationbe‐
tweenelements
Notdeployed‐
Shadowsgeneratedby
rotatedflaps
Theadaptivepropertiesofthisconceptwerechosentobebothauto‐reactive(coat‐
ing,flaps)andmechanicallyoperatedbythebuildingoccupants(deformation,flaps).
2.3.ParametricDesignoftheConcept
Asabiology‐pushapproachwasfollowedforthedesignconcept,noparticular
buildingenveloperequirementsweredefinedasspecificationsforthefinaldesign.How‐
ever,ithadtobemultifunctionalregardingheat,light,andairmanagement.Oncethe
functionswerecharacterized,consideringclearrequirements,aspecificdesigncouldbe
proposed.
Thesefunctionsaresometimesimplementedthroughinterdependentparameters;
asanexplorationbeforeafinalsetofparameters,numerousparametersandtheir
respectivevalueswereproposed(Table3).
Table3.Listofdesignparametersthatwereconsideredfortheconceptandtheirrespectivepossible
values.
ElementsParametersPossibleValues
Mesh
PatternTriangular/radial/squared/fabrics/ropes
MaterialSilicon/rubber/O‐ringjoints/chains
Scaleofdeformation 1cm/10cm/100cm
Typeoftensionforce Point/surfacearea/linear
Numberoftensionforces Single/multiple
Tiltoftension Centimeters/decimeters/meters
Direction Onward/outward
Adaptive coating less
absorbing with threshold
temperature + decrease in
temperature with shadows
Shadows generated
by rotated flaps
Air passing through
if bases are hollowed
Not deployed Adaptive coating - -
Deformed
Energies2022,15,xFORPEERREVIEW5of19


Table2.Managedfunctionsaccordingtoconfigurations.Forvisualdisplay,flapsarewhiteand
baseelementsaredarkgrey.
MeshFlapHeatLightAir
Flat


Deployed


Adaptivecoatinglessab‐
sorbingwiththreshold
temperature
+decreaseintemperature
withshadows
Shadowsgeneratedby
rotatedflaps
Airpassingthrough
ifbasesarehollowed
NotdeployedAdaptivecoating  ‐ ‐
Deformed


Deployed


Adaptivecoating+de‐
creaseintemperaturewith
shadows
Shadowsgeneratedby
rotatedflaps
Airpassingthrough
thegapscreatedthe
deformationbe‐
tweenelements
Notdeployed‐
Shadowsgeneratedby
rotatedflaps
Theadaptivepropertiesofthisconceptwerechosentobebothauto‐reactive(coat‐
ing,flaps)andmechanicallyoperatedbythebuildingoccupants(deformation,flaps).
2.3.ParametricDesignoftheConcept
Asabiology‐pushapproachwasfollowedforthedesignconcept,noparticular
buildingenveloperequirementsweredefinedasspecificationsforthefinaldesign.How‐
ever,ithadtobemultifunctionalregardingheat,light,andairmanagement.Oncethe
functionswerecharacterized,consideringclearrequirements,aspecificdesigncouldbe
proposed.
Thesefunctionsaresometimesimplementedthroughinterdependentparameters;
asanexplorationbeforeafinalsetofparameters,numerousparametersandtheir
respectivevalueswereproposed(Table3).
Table3.Listofdesignparametersthatwereconsideredfortheconceptandtheirrespectivepossible
values.
ElementsParametersPossibleValues
Mesh
PatternTriangular/radial/squared/fabrics/ropes
MaterialSilicon/rubber/O‐ringjoints/chains
Scaleofdeformation 1cm/10cm/100cm
Typeoftensionforce Point/surfacearea/linear
Numberoftensionforces Single/multiple
Tiltoftension Centimeters/decimeters/meters
Direction Onward/outward
Deployed
Energies2022,15,xFORPEERREVIEW5of19


Table2.Managedfunctionsaccordingtoconfigurations.Forvisualdisplay,flapsarewhiteand
baseelementsaredarkgrey.
MeshFlapHeatLightAir
Flat


Deployed


Adaptivecoatinglessab‐
sorbingwiththreshold
temperature
+decreaseintemperature
withshadows
Shadowsgeneratedby
rotatedflaps
Airpassingthrough
ifbasesarehollowed
NotdeployedAdaptivecoating  ‐ ‐
Deformed


Deployed


Adaptivecoating+de‐
creaseintemperaturewith
shadows
Shadowsgeneratedby
rotatedflaps
Airpassingthrough
thegapscreatedthe
deformationbe‐
tweenelements
Notdeployed‐
Shadowsgeneratedby
rotatedflaps
Theadaptivepropertiesofthisconceptwerechosentobebothauto‐reactive(coat‐
ing,flaps)andmechanicallyoperatedbythebuildingoccupants(deformation,flaps).
2.3.ParametricDesignoftheConcept
Asabiology‐pushapproachwasfollowedforthedesignconcept,noparticular
buildingenveloperequirementsweredefinedasspecificationsforthefinaldesign.How‐
ever,ithadtobemultifunctionalregardingheat,light,andairmanagement.Oncethe
functionswerecharacterized,consideringclearrequirements,aspecificdesigncouldbe
proposed.
Thesefunctionsaresometimesimplementedthroughinterdependentparameters;
asanexplorationbeforeafinalsetofparameters,numerousparametersandtheir
respectivevalueswereproposed(Table3).
Table3.Listofdesignparametersthatwereconsideredfortheconceptandtheirrespectivepossible
values.
ElementsParametersPossibleValues
Mesh
PatternTriangular/radial/squared/fabrics/ropes
MaterialSilicon/rubber/O‐ringjoints/chains
Scaleofdeformation 1cm/10cm/100cm
Typeoftensionforce Point/surfacearea/linear
Numberoftensionforces Single/multiple
Tiltoftension Centimeters/decimeters/meters
Direction Onward/outward
Adaptive coating +
decrease in temperature
with shadows
Shadows generated
by rotated flaps Air passing through
the gaps created the
deformation between
elements
Not deployed - Shadows generated
by rotated flaps
2.3. Parametric Design of the Concept
As a biology-push approach was followed for the design concept, no particular building
envelope requirements were defined as specifications for the final design.
However, it had
to be multifunctional regarding heat, light, and air management. Once the functions were
characterized, considering clear requirements, a specific design could be proposed.
These functions are sometimes implemented through interdependent parameters;
as an
exploration before a final set of parameters, numerous parameters and their respective
values were proposed (Table 3).
Table 3.
List of design parameters that were considered for the concept and their respective
possible values.
Elements Parameters Possible Values
Mesh
Pattern Triangular/radial/squared/fabrics/ropes
Material Silicon/rubber/O-ring joints/chains
Scale of deformation 1 cm/10 cm/100 cm
Type of tension force Point/surface area/linear
Number of tension forces Single/multiple
Tilt of tension Centimeters/decimeters/meters
Direction Onward/outward
Piloting setting Manual/automatic
Piloting functioning Mechanical/electrical/chemical
Base and flaps
Material Alloy/metal/wood/clay-based
material/polymers
Size scales 1 cm/10 cm
Homogeneity Plain/hollowed

Energies 2022,15, 891 6 of 19
Table 3. Cont.
Elements Parameters Possible Values
Flaps
Axis of rotation Lateral/central
Size Smaller than base/larger than base
Shape Round/polygonal (triangular, rectangular,
hexagonal)
Homogeneity Plain/hollowed
Coating Yes/no
Piloting setting Manual/automatic/coupled with
deformation/decoupled
Piloting functioning Mechanical/electrical/chemical
Distance between each other None/smaller than size of flaps/larger
The functions brought by the different values of the parameters are various. To narrow
the study to a limited number of designs, derivatives of the concept were prototyped with
the following elements:
•Form of the mesh elements: size, shape, orientation, and the axis of rotation;
•
The total scale of the design: minimum size for representative results in terms of the
physical phenomena.
Form-finding and visual representation helped define the form of the mesh elements.
The hexagonal shape was chosen over squares as it removed physical collisions between
opened flaps when the mesh was deformed, as shown in Figure 2a. Projected light simula-
tions foreshadowed various scenarios when changing the orientation of the flaps along the
mesh; hence, this parameter was selected and technically implemented into the prototype
by designing a notched system (Figure 2b). Last, the size of the elements was arbitrarily set
as a trade-off between the minimum size for ease of manufacture and the maximum accept-
able size by the occupants in terms of view towards the exterior environment (Figure 2c).
Energies 2022, 15, x FOR PEER REVIEW 6 of 18
Form-finding and visual representation helped define the form of the mesh elements.
The hexagonal shape was chosen over squares as it removed physical collisions between
opened flaps when the mesh was deformed, as shown in Figure 2a. Projected light simu-
lations foreshadowed various scenarios when changing the orientation of the flaps along
the mesh; hence, this parameter was selected and technically implemented into the proto-
type by designing a notched system (Figure 2b). Last, the size of the elements was arbi-
trarily set as a trade-off between the minimum size for ease of manufacture and the max-
imum acceptable size by the occupants in terms of view towards the exterior environment
(Figure 2c).
(a) (b) (c)
Figure 2. All computer-aided images were made using Rhinoceros Grasshopper software. (a) Visual
representation of potential collisions during deformations using squares vs. hexagons as base ele-
ments. (b) Exploration of different positions of flaps. The interchangeability was kept possible for
the prototype using a 3D-printed notch-system as a flap holder, insertable into an aluminum frame
as shown in the bottom images. (c) Qualitative determination elements with a fish-eye view from
behind glazing. HD file generated using the Ladybug component.
To obtain significant results in terms of physical phenomenon and overpass scale
effects, mostly regarding air flows and the edge effect on thermal losses, the total design
surface area was set to an arbitrary 1 m
2
for the experimentation.
All parameters chosen above are the result of feasibility considerations. They are
trade-offs between the time of prototyping, cost, and complexity of construction tech-
niques. The piloting of the flaps, for instance, was chosen to be mechanical, and manually
operated.
3. Experimentation on a Prototype: Stegos Design
The concept presented in Part 2 combines multiple functions that are co-dependent
and rely on a distortion coupled with deployment and auto-reactive paint. To separately
assess the contribution of deployment and distortion on the thermal, light, and air prop-
erties, the authors prototyped a first version, called Stegos, with only rotating coated flaps.
Three possible architectural integration configurations are considered (see Figure 3):
• ‘Opaque’ configuration, as part of an opaque wall;
• ‘Glazing’ configuration, as a smart protection envelope put in front of windows;
• ‘Envelope’ configuration, as an openable envelope, equivalent to a window. Alt-
hough complex to implement, it would offer multiple regulation assets for warm cli-
mates.
Figure 2.
All computer-aided images were made using Rhinoceros Grasshopper software.
(a) Visual
representation of potential collisions during deformations using squares vs. hexagons as base
elements. (
b
) Exploration of different positions of flaps. The interchangeability was kept possible for
the prototype using a 3D-printed notch-system as a flap holder, insertable into an aluminum frame
as shown in the bottom images. (
c
) Qualitative determination elements with a fish-eye view from
behind glazing. HD file generated using the Ladybug component.
To obtain significant results in terms of physical phenomenon and overpass scale
effects, mostly regarding air flows and the edge effect on thermal losses, the total design
surface area was set to an arbitrary 1 m2for the experimentation.

Energies 2022,15, 891 7 of 19
All parameters chosen above are the result of feasibility considerations. They are
trade-offs between the time of prototyping, cost, and complexity of construction techniques.
The piloting of the flaps, for instance, was chosen to be mechanical, and manually operated.
3. Experimentation on a Prototype: Stegos Design
The concept presented in Part 2 combines multiple functions that are co-dependent and
rely on a distortion coupled with deployment and auto-reactive paint. To separately assess
the contribution of deployment and distortion on the thermal, light, and air properties,
the authors
prototyped a first version, called Stegos, with only rotating coated flaps. Three
possible architectural integration configurations are considered (see Figure 3):
•‘Opaque’ configuration, as part of an opaque wall;
•‘Glazing’ configuration, as a smart protection envelope put in front of windows;
•
‘Envelope’ configuration, as an openable envelope, equivalent to a window. Although
complex to implement, it would offer multiple regulation assets for warm climates.
Energies 2022, 15, x FOR PEER REVIEW 7 of 18
(a) (b) (c)
Figure 3. (a) ‘Opaque’ configuration. (b) ‘Glazing’ configuration. (c) ‘Envelope’ configuration.
3.1. Prototyping
The prototype was manufactured to be modular and easily switched from one
configuration (as described in Figure 3) to another. It was designed as an assembly of
aluminum pieces and 3D-printed material. Schematics and photos of all pieces are shown
in Figure 4.
(a)
(b)
Figure 4. (a) Schematics of the notched system, flaps, and the aluminum frame. (b) Photographs of
the prototype elements.
A 1 m
2
aluminum plate, 4 mm thick, was first water-jet cut as a structural support.
The cutting included the edges of the frame, hexagonal holes to let light and air go through
for the ‘glazing’ and ‘envelope’ configurations, and oval-shaped holes to insert the
rotating flap system.
The notch system, designed to change the position and angles of the flaps according
to the time of day, season, or year, was 3D-printed with ABS. It is made of two pieces, one
for inserting the flaps and a second to be inserted into the aluminum frame. Both of them
have ridges to create a controlled manual rotation 15° by 15°, and they are held together
with a metal pin. Small edges on the side of the bottom piece ensure a mechanical holding
into the aluminum frame.
The flaps were laser-cut into 1 mm thick aluminum plates. An overhang on one side
of the hexagonal piece allows insertion into the notched system slit without using screws
or glue. They were painted with thermochromic paint, as explained in the next section.
Figure 3. (a) ‘Opaque’ configuration. (b) ‘Glazing’ configuration. (c) ‘Envelope’ configuration.
3.1. Prototyping
The prototype was manufactured to be modular and easily switched from one config-
uration (as described in Figure 3) to another. It was designed as an assembly of aluminum
pieces and 3D-printed material. Schematics and photos of all pieces are shown in Figure 4.
Energies 2022, 15, x FOR PEER REVIEW 7 of 18
(a) (b) (c)
Figure 3. (a) ‘Opaque’ configuration. (b) ‘Glazing’ configuration. (c) ‘Envelope’ configuration.
3.1. Prototyping
The prototype was manufactured to be modular and easily switched from one
configuration (as described in Figure 3) to another. It was designed as an assembly of
aluminum pieces and 3D-printed material. Schematics and photos of all pieces are shown
in Figure 4.
(a)
(b)
Figure 4. (a) Schematics of the notched system, flaps, and the aluminum frame. (b) Photographs of
the prototype elements.
A 1 m
2
aluminum plate, 4 mm thick, was first water-jet cut as a structural support.
The cutting included the edges of the frame, hexagonal holes to let light and air go through
for the ‘glazing’ and ‘envelope’ configurations, and oval-shaped holes to insert the
rotating flap system.
The notch system, designed to change the position and angles of the flaps according
to the time of day, season, or year, was 3D-printed with ABS. It is made of two pieces, one
for inserting the flaps and a second to be inserted into the aluminum frame. Both of them
have ridges to create a controlled manual rotation 15° by 15°, and they are held together
with a metal pin. Small edges on the side of the bottom piece ensure a mechanical holding
into the aluminum frame.
The flaps were laser-cut into 1 mm thick aluminum plates. An overhang on one side
of the hexagonal piece allows insertion into the notched system slit without using screws
or glue. They were painted with thermochromic paint, as explained in the next section.
Figure 4.
(
a
) Schematics of the notched system, flaps, and the aluminum frame. (
b
) Photographs of
the prototype elements.

Energies 2022,15, 891 8 of 19
A1m
2
aluminum plate, 4 mm thick, was first water-jet cut as a structural support.
The cutting included the edges of the frame, hexagonal holes to let light and air go through
for the ‘glazing’ and ‘envelope’ configurations, and oval-shaped holes to insert the rotating
flap system.
The notch system, designed to change the position and angles of the flaps according
to the time of day, season, or year, was 3D-printed with ABS. It is made of two pieces, one
for inserting the flaps and a second to be inserted into the aluminum frame. Both of them
have ridges to create a controlled manual rotation 15
◦
by 15
◦
, and they are held together
with a metal pin. Small edges on the side of the bottom piece ensure a mechanical holding
into the aluminum frame.
The flaps were laser-cut into 1 mm thick aluminum plates. An overhang on one side
of the hexagonal piece allows insertion into the notched system slit without using screws
or glue. They were painted with thermochromic paint, as explained in the next section.
The assembly of these elements forms the ‘glazing’ and ‘envelope‘ Stegos basic con-
figurations. For the ‘opaque’ one, a 1 m
2
plain plate of 1 mm thick aluminum was added
behind the system.
3.2. Thermochromic Coating
The auto-reactivity of the Stegos, a feature inspired by the emissive properties of the
butterfly, was technologically translated using a thermochromic paint, i.e., whose color
changes with temperature. Different pairs of colors, such as brown cream or burgundy
yellow, were formulated for a temperature threshold around 45
◦
C, before settling with a
blue white combination for the prototype. The reflectance of the thermochromic paint was
measured at 20
◦
C and 60
◦
C. A spectrophotometer measuring the reflected light (specular
and diffuse) was used on samples of coated aluminum plates for a wavelength between
200 nm and 2500 nm. The deduced absorption coefficient (
α
= 1
−
R) is shown in Figure 5.
The change in color from blue to white when temperature increases is not instantaneous,
but rather progressive between 40 ◦C and 50 ◦C.
Energies 2022, 15, x FOR PEER REVIEW 8 of 18
The assembly of these elements forms the ‘glazing’ and ‘envelope‘ Stegos basic
configurations. For the ‘opaque’ one, a 1 m
2
plain plate of 1 mm thick aluminum was
added behind the system.
3.2. Thermochromic Coating
The auto-reactivity of the Stegos, a feature inspired by the emissive properties of the
butterfly, was technologically translated using a thermochromic paint, i.e., whose color
changes with temperature. Different pairs of colors, such as brown cream or burgundy
yellow, were formulated for a temperature threshold around 45 °C, before settling with a
blue white combination for the prototype. The reflectance of the thermochromic paint was
measured at 20 °C and 60 °C. A spectrophotometer measuring the reflected light (specular
and diffuse) was used on samples of coated aluminum plates for a wavelength between
200 nm and 2500 nm. The deduced absorption coefficient (α = 1 − R) is shown in Figure 5.
The change in color from blue to white when temperature increases is not instantaneous,
but rather progressive between 40 °C and 50 °C.
Figure 5. Absorption coefficient of paint measured at 20 °C and 60 °C. The black arrow on the graph
shows a high variation in the coefficient in the visible spectrum.
When changing color from blue to white, the coating absorptivity naturally decreases
in the visible spectrum (40% average decrease between 400 nm and 700 nm). As this wave-
length range accounts for 40% of the total solar spectrum energy [28], such a change on a
thermochromic-coated material should have a significant impact on its solar thermal ab-
sorption. The absorption coefficient is lower as well in the near-infrared wavelength
range, albeit not as significant. Therefore, when exposed to constant solar radiation, the
expected behavior of a coated sample is a slowdown in the increase in temperature around
the threshold temperature.
3.3. Integration in Test Box Protocol Experimentation
To observe realistic behavior as a skin, the prototype was integrated into an insu-
lated, airtight box specifically designed for experiments in real climate conditions.
3.3.1. Test Box Design
The test box was designed to have an internal exact 1 m
3
volume (Figure 6). It was
composed of six walls, one of them being interchangeable, i.e., destined for tested system
façades. The other five walls were made of 8 cm of polyurethane insulation, sandwiched
Figure 5.
Absorption coefficient of paint measured at 20
◦
C and 60
◦
C. The black arrow on the graph
shows a high variation in the coefficient in the visible spectrum.
When changing color from blue to white, the coating absorptivity naturally decreases
in the visible spectrum (40% average decrease between 400 nm and 700 nm). As this
wavelength range accounts for 40% of the total solar spectrum energy [
28
], such a change
on a thermochromic-coated material should have a significant impact on its solar thermal
absorption. The absorption coefficient is lower as well in the near-infrared wavelength

Energies 2022,15, 891 9 of 19
range, albeit not as significant. Therefore, when exposed to constant solar radiation,
the expected
behavior of a coated sample is a slowdown in the increase in temperature
around the threshold temperature.
3.3. Integration in Test Box Protocol Experimentation
To observe realistic behavior as a skin, the prototype was integrated into an insulated,
airtight box specifically designed for experiments in real climate conditions.
3.3.1. Test Box Design
The test box was designed to have an internal exact 1 m
3
volume (Figure 6). It was
composed of six walls, one of them being interchangeable, i.e., destined for tested system
façades. The other five walls were made of 8 cm of polyurethane insulation, sandwiched
between oriented strand board (OSB). For structural purposes, aluminum profiles were
added on their outer sides between insulation and OSB, adding an air gap of 40 mm.
Energies 2022, 15, x FOR PEER REVIEW 9 of 18
between oriented strand board (OSB). For structural purposes, aluminum profiles were
added on their outer sides between insulation and OSB, adding an air gap of 40 mm.
(a) (b)
Figure 6. (a) Diagram of the tests box with the Stegos as an opaque wall. (b) Photograph of the test
box with the Stegos integrated on one of the façades.
Several actions were made to avoid deterioration of the box with time owing to hu-
midity or heavy rains while experimentations were ongoing: external OSBs were var-
nished, the top of the box was covered with a waterproof membrane, and a silicone joint
was applied on several points to improve airtightness. A roof overhang was added as
well, small enough to not create a shadow on the tested façade that would interfere with
the measurements.
To be able to test the box in all orientations and to make it rotative, the test box was
equipped with four steering wheels. An electric box with ventilation grids was screwed
on one of the external sides to hold the monitoring instruments away from the internal
conditions of the test box and protect them from climatic conditions. In fact, the issue of
having them inside the box would be non-negligible disturbances on the test box internal
conditions owing to generated heat.
The design of the test box allows the experiments of the Stegos in all three configura-
tions, as illustrated in Figure 3. The ‘Glazing’ configuration requires replacing the ply-
wood with a transparent wall (a synthetic glass such as Plexiglas was chosen) airtightly
plastered on the test box, on which the Stegos is placed. To switch to the ‘Envelope’ con-
figuration, only removing the transparent layer is needed.
3.3.2. Experimental Protocol
To monitor the weather conditions, sensors for the external air temperature, the
wind, and the solar irradiance on planar surfaces were installed. Two configurations’ ex-
periments are presented in this article: the ‘Glazing’ and the ‘Opaque’ configurations for
varying angles of rotation of flaps of 0°, 45°, and 90°.
The monitoring of the test box and the Stegos behaviors varied from one configura-
tion to another as their targeted functionalities are different. When the Stegos is used as
part of an opaque wall, measurements of temperature and heat-flows were inside the test
box and at different layers of the tested façade. The list of all sensors is given in Table 4.
Figure 6.
(
a
) Diagram of the tests box with the Stegos as an opaque wall. (
b
) Photograph of the test
box with the Stegos integrated on one of the façades.
Several actions were made to avoid deterioration of the box with time owing to humid-
ity or heavy rains while experimentations were ongoing: external OSBs were varnished,
the top of the box was covered with a waterproof membrane, and a silicone joint was
applied on several points to improve airtightness. A roof overhang was added as well,
small enough to not create a shadow on the tested façade that would interfere with the
measurements.
To be able to test the box in all orientations and to make it rotative, the test box was
equipped with four steering wheels. An electric box with ventilation grids was screwed
on one of the external sides to hold the monitoring instruments away from the internal
conditions of the test box and protect them from climatic conditions. In fact, the issue of
having them inside the box would be non-negligible disturbances on the test box internal
conditions owing to generated heat.
The design of the test box allows the experiments of the Stegos in all three configura-
tions, as illustrated in Figure 3. The ‘Glazing’ configuration requires replacing the plywood
with a transparent wall (a synthetic glass such as Plexiglas was chosen) airtightly plastered
on the test box, on which the Stegos is placed. To switch to the ‘Envelope’ configuration,
only removing the transparent layer is needed.
3.3.2. Experimental Protocol
To monitor the weather conditions, sensors for the external air temperature, the wind,
and the solar irradiance on planar surfaces were installed. Two configurations’ experiments
are presented in this article: the ‘Glazing’ and the ‘Opaque’ configurations for varying
angles of rotation of flaps of 0◦, 45◦, and 90◦.

Energies 2022,15, 891 10 of 19
The monitoring of the test box and the Stegos behaviors varied from one configuration
to another as their targeted functionalities are different. When the Stegos is used as part of
an opaque wall, measurements of temperature and heat-flows were inside the test box and
at different layers of the tested façade. The list of all sensors is given in Table 4.
Table 4. List of installed sensors on the test bench.
Parameter Type of Sensor Location Uncertainty
Solar irradiance on planar
surfaces
SMP3 pyranometer
(0–1600 W/m2)
1 on plane of tested façade
1 on plane of the flaps 10 W/m2
Wind speed Cup wind sensor
(0–35 m/s)
1 outside (plane of tested façade,
1.8 m high) 0.2 m/s
Ambient temperature Resistance temperature
detector PT100
1 outside (0.2 m away from box,
0.7 m high)
1 inside (center of box, 0.5 m high)
0.5 ◦C
Heat flow Copper heat flux sensor (with
tangential gradients)
11 in layers of the tested façade
(Figure 7)3%
Surface temperature Thermocouple Type K 16 in layers of the tested façade
(Figure 7)0.5 ◦C
Energies 2022, 15, x FOR PEER REVIEW 10 of 18
Table 4. List of installed sensors on the test bench.
Parameter Type of Sensor Location Uncertainty
Solar irradiance on pla-
nar surfaces
SMP3 pyranometer
(0–1600 W/m
2
)
1 on plane of tested façade
1 on plane of the flaps 10 W/m
2
Wind speed Cup wind sensor
(0–35 m/s) 1 outside (plane of tested façade, 1.8 m high) 0.2 m/s
Ambient temperature Resistance temperature detec-
tor PT100
1 outside (0.2 m away from box, 0.7 m high)
1 inside (center of box, 0.5 m high) 0.5 °C
Heat flow Copper heat flux sensor (with
tangential gradients) 11 in layers of the tested façade (Figure 7) 3%
Surface temperature Thermocouple Type K 16 in layers of the tested façade (Figure 7) 0.5 °C
Figure 7. Repartition and nomenclature of temperature (T) and heat flux (HF) sensors using a top-
view diagram of the Stegos + wall of the test box.
Thermocouple sensors taped on flaps and welded on all heat flux sensors measured
surface temperature where heat flows are measured. Copper foil heat flux sensors with
tangential gradients of varying sizes (surfaces from 3 mm × 3 mm to 30 mm × 30 mm,
thickness of 5 mm) were duplicated on some layers; even though these sensors were all
calibrated beforehand, ‘incorrect’ measurements were still possible because of several fac-
tors such as an improper set-up of the sensors or unpredictable issues during experimen-
tation. The repartition of the sensors is illustrated in Figure 7. Note that a 5 mm foam was
added between the aluminum plate and the plywood to ensure no air gap.
To assess the ‘Glazing’ configuration, the shading effect of the Stegos flaps was as-
sessed with a camera fixed inside the test box, looking at the bottom surface in order to
take a time-lapse of the projected light and shadow throughout the day.
The testing procedure starts with the installation of the presented test box equipped
with the Stegos outside in Talence (close to Bordeaux), France. The typical measurement
lasts 3 to 4 days with the objective to have 2 full days. The measurements were carried
out between 1 August and 30 November of 2021 with south and south-west orientations
and configurations as ‘opaque’ and ‘glazing’. A series of 10 separated sequences were
run.
3.4. Measurements
The flaps showed an effective color change when the surface temperature reached a
temperature beyond 45 °C (Figure 8). Owing to the use of aluminum as a base material
for the flaps, i.e., quite absorptive (see Figure 5) and with high thermal conductivity (λ
alu-
minum
= 230 W/m·K), a decrease or increase in very short time cycles of the solar radiation—
owing to a temporary cloud cover, for instance—had an immediate visual effect on the
surface color.
Figure 7.
Repartition and nomenclature of temperature (T) and heat flux (HF) sensors using a
top-view diagram of the Stegos + wall of the test box.
Thermocouple sensors taped on flaps and welded on all heat flux sensors measured
surface temperature where heat flows are measured. Copper foil heat flux sensors with
tangential gradients of varying sizes (surfaces from 3 mm
×
3 mm to 30 mm
×
30 mm,
thickness of 5 mm) were duplicated on some layers; even though these sensors were all cal-
ibrated beforehand, ‘incorrect’ measurements were still possible because of several factors
such as an improper set-up of the sensors or unpredictable issues during experimentation.
The repartition of the sensors is illustrated in Figure 7. Note that a 5 mm foam was added
between the aluminum plate and the plywood to ensure no air gap.
To assess the ‘Glazing’ configuration, the shading effect of the Stegos flaps was assessed
with a camera fixed inside the test box, looking at the bottom surface in order to take a
time-lapse of the projected light and shadow throughout the day.
The testing procedure starts with the installation of the presented test box equipped
with the Stegos outside in Talence (close to Bordeaux), France. The typical measurement
lasts 3 to 4 days with the objective to have 2 full days. The measurements were carried out
between 1 August and 30 November of 2021 with south and south-west orientations and
configurations as ‘opaque’ and ‘glazing’. A series of 10 separated sequences were run.
3.4. Measurements
The flaps showed an effective color change when the surface temperature reached a
temperature beyond 45
◦
C (Figure 8). Owing to the use of aluminum as a base material
for the flaps, i.e., quite absorptive (see Figure 5) and with high thermal conductivity
(λaluminum = 230 W/m·K)
, a decrease or increase in very short time cycles of the solar

Energies 2022,15, 891 11 of 19
radiation—owing to a temporary cloud cover, for instance—had an immediate visual effect
on the surface color.
Energies 2022, 15, x FOR PEER REVIEW 11 of 18
Figure 8. Photo of the test box and temperature measurements of flaps’ inner surfaces performed
on the afternoon of 9 August 2021 in Bordeaux, France. Flaps are rotated differently on areas 1 (angle
= 30°) and 2 (angle = 0°) and the test-box orientation is west. The red line on the graph highlights the
45 °C temperature threshold for the flaps to change their color. T
ext
is the external air temperature.
3.4.1. ‘Opaque’ Configuration
Measurements were performed using different test box and flap configurations. The
test box was successively oriented east, south, and west. Different positions and angles for
the flaps were tested:
• Position as a solar cap, i.e., the rotation axis is horizontal and on top of the base. Ver-
tical position, i.e., the rotation axis is vertical. This configuration results in larger
shadows at the beginning and end of the day when the test box is oriented south,
whereas the solar cap position will have larger shadows during mid-day;
• Angle of rotation of claps of 0°, 45°, and 90°.
Data measured during several days with closed flaps and test box oriented south are
given in Figure 9. The total inertia of the test box can be observed by identifying the phase
shift between the inside and outside ambiant temperatures. The heatflows measured in
different layers of the tested wall (Stegos + wall) decrease from the external layer to the
internal layer. This difference is particulary high between the external surfaces of the
aluminum and the plywood (HF_al_e and HF_w_e, respectively). It can be explained by
the fact that the heat collected by the flaps is transferred to the 1 mm aluminum sheet and
then conducted to its perimeter, owing to its high conductivity. The heat is then dissipated
by convection. Accordingly, we will improve the experimental design by adding an
insulation frame to the aluminum sheets.
Figure 9. (Top left) Incident solar radiation, (bottom left) internal and external air temperatures,
(top right) heat flows, and (bottom right) associated temperatures in the tested façade from No-
vember 15 to November 18, 2021. Test box oriented south, angle of flaps = 0°.
Figure 8.
Photo of the test box and temperature measurements of flaps’ inner surfaces performed
on the afternoon of 9 August 2021 in Bordeaux, France. Flaps are rotated differently on areas 1
(angle = 30◦)
and 2 (angle = 0
◦
) and the test-box orientation is west. The red line on the graph
highlights the 45
◦
C temperature threshold for the flaps to change their color. T
ext
is the external air
temperature.
3.4.1. ‘Opaque’ Configuration
Measurements were performed using different test box and flap configurations.
The test
box was successively oriented east, south, and west. Different positions and angles for the
flaps were tested:
•
Position as a solar cap, i.e., the rotation axis is horizontal and on top of the base.
Vertical position, i.e., the rotation axis is vertical. This configuration results in larger
shadows at the beginning and end of the day when the test box is oriented south,
whereas the solar cap position will have larger shadows during mid-day;
•Angle of rotation of claps of 0◦, 45◦, and 90◦.
Data measured during several days with closed flaps and test box oriented south
are given in Figure 9. The total inertia of the test box can be observed by identifying the
phase shift between the inside and outside ambiant temperatures. The heatflows measured
in different layers of the tested wall (Stegos + wall) decrease from the external layer to
the internal layer. This difference is particulary high between the external surfaces of the
aluminum and the plywood (HF_al_e and HF_w_e, respectively). It can be explained by the
fact that the heat collected by the flaps is transferred to the 1 mm aluminum sheet and then
conducted to its perimeter, owing to its high conductivity. The heat is then dissipated by
convection. Accordingly, we will improve the experimental design by adding an insulation
frame to the aluminum sheets.

Energies 2022,15, 891 12 of 19
Energies 2022, 15, x FOR PEER REVIEW 11 of 18
Figure 8. Photo of the test box and temperature measurements of flaps’ inner surfaces performed
on the afternoon of 9 August 2021 in Bordeaux, France. Flaps are rotated differently on areas 1 (angle
= 30°) and 2 (angle = 0°) and the test-box orientation is west. The red line on the graph highlights the
45 °C temperature threshold for the flaps to change their color. T
ext
is the external air temperature.
3.4.1. ‘Opaque’ Configuration
Measurements were performed using different test box and flap configurations. The
test box was successively oriented east, south, and west. Different positions and angles for
the flaps were tested:
• Position as a solar cap, i.e., the rotation axis is horizontal and on top of the base. Ver-
tical position, i.e., the rotation axis is vertical. This configuration results in larger
shadows at the beginning and end of the day when the test box is oriented south,
whereas the solar cap position will have larger shadows during mid-day;
• Angle of rotation of claps of 0°, 45°, and 90°.
Data measured during several days with closed flaps and test box oriented south are
given in Figure 9. The total inertia of the test box can be observed by identifying the phase
shift between the inside and outside ambiant temperatures. The heatflows measured in
different layers of the tested wall (Stegos + wall) decrease from the external layer to the
internal layer. This difference is particulary high between the external surfaces of the
aluminum and the plywood (HF_al_e and HF_w_e, respectively). It can be explained by
the fact that the heat collected by the flaps is transferred to the 1 mm aluminum sheet and
then conducted to its perimeter, owing to its high conductivity. The heat is then dissipated
by convection. Accordingly, we will improve the experimental design by adding an
insulation frame to the aluminum sheets.
Figure 9. (Top left) Incident solar radiation, (bottom left) internal and external air temperatures,
(top right) heat flows, and (bottom right) associated temperatures in the tested façade from No-
vember 15 to November 18, 2021. Test box oriented south, angle of flaps = 0°.
Figure 9.
(
Top left
) Incident solar radiation, (
bottom left
) internal and external air temperatures,
(top right)
heat flows, and (
bottom right
) associated temperatures in the tested façade from Novem-
ber 15 to November 18, 2021. Test box oriented south, angle of flaps = 0◦.
A direct comparison between the two configurations is shown in Figure 10. For similar
days (maximum solar radiation and outside temperture around 800 W/m
2
and 23
◦
C,
respectively), a difference of about 13% can be observed on heat flows measured at the
inner surface of the Stegos aluminum during sunlight hours. This could mean that the solar
cap configuration—horizontal axis of rotation and 90
◦
angle of flaps—transfers more heat
into the test box at this time of the year; however, it is not consistent with the measured
internal air temperatures, which appear to be very similar. As the measurements are shown,
it is not possible to determine whether the Stegos has an insignificant impact on the test
box conditions or whether the external conditions from the previous day are still having
an impact.
Energies 2022, 15, x FOR PEER REVIEW 12 of 18
A direct comparison between the two configurations is shown in Figure 10. For
similar days (maximum solar radiation and outside temperture around 800 W/m
2
and 23
°C, respectively), a difference of about 13% can be observed on heat flows measured at the
inner surface of the Stegos aluminum during sunlight hours. This could mean that the solar
cap configuration—horizontal axis of rotation and 90° angle of flaps—transfers more heat
into the test box at this time of the year; however, it is not consistent with the measured
internal air temperatures, which appear to be very similar. As the measurements are
shown, it is not possible to determine whether the Stegos has an insignificant impact on
the test box conditions or whether the external conditions from the previous day are still
having an impact.
Figure 10. Layering of measurements performed on the test box during two separate days. Incident
solar radiation, air temperatures, and heat flows. Measurements on 14 October 2021: closed flaps.
Measurements on 26 October 2021: opened flap with a 90° angle, along a horizontal rotation axis
(solar cap configuration).
3.4.2. ‘Glazing’ Configuration
Photos of the experimentation set for the Stegos ‘glazing’ are shown in Figure 11.
Pictures of the projected light and shadow on the bottom surface every 10 min of the day
were taken using the camera fixed on top of the test box. The configuration sets for the
test box were identical to the ones used for the experimental protocol of the ‘opaque’ con-
figuration.
Figure 11. Photos of the Stegos ‘glazing’ configuration on the test box with claps positioned as solar
caps and opened to a 90° angle. Camera fixed on the roof wall of the test box.
The difference illustrated in Figure 12 between flap angles of 45° and 90° is visible
and expected with the sun elevation in November in France.
Figure 10.
Layering of measurements performed on the test box during two separate days. Incident
solar radiation, air temperatures, and heat flows. Measurements on 14 October 2021: closed flaps.
Measurements on 26 October 2021: opened flap with a 90
◦
angle, along a horizontal rotation axis
(solar cap configuration).
3.4.2. ‘Glazing’ Configuration
Photos of the experimentation set for the Stegos ‘glazing’ are shown in Figure 11. Pic-
tures of the projected light and shadow on the bottom surface every 10 min of the day were
taken using the camera fixed on top of the test box. The configuration sets for the test box
were identical to the ones used for the experimental protocol of the
‘opaque’ configuration.

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Energies 2022, 15, x FOR PEER REVIEW 12 of 18
A direct comparison between the two configurations is shown in Figure 10. For
similar days (maximum solar radiation and outside temperture around 800 W/m
2
and 23
°C, respectively), a difference of about 13% can be observed on heat flows measured at the
inner surface of the Stegos aluminum during sunlight hours. This could mean that the solar
cap configuration—horizontal axis of rotation and 90° angle of flaps—transfers more heat
into the test box at this time of the year; however, it is not consistent with the measured
internal air temperatures, which appear to be very similar. As the measurements are
shown, it is not possible to determine whether the Stegos has an insignificant impact on
the test box conditions or whether the external conditions from the previous day are still
having an impact.
Figure 10. Layering of measurements performed on the test box during two separate days. Incident
solar radiation, air temperatures, and heat flows. Measurements on 14 October 2021: closed flaps.
Measurements on 26 October 2021: opened flap with a 90° angle, along a horizontal rotation axis
(solar cap configuration).
3.4.2. ‘Glazing’ Configuration
Photos of the experimentation set for the Stegos ‘glazing’ are shown in Figure 11.
Pictures of the projected light and shadow on the bottom surface every 10 min of the day
were taken using the camera fixed on top of the test box. The configuration sets for the
test box were identical to the ones used for the experimental protocol of the ‘opaque’ con-
figuration.
Figure 11. Photos of the Stegos ‘glazing’ configuration on the test box with claps positioned as solar
caps and opened to a 90° angle. Camera fixed on the roof wall of the test box.
The difference illustrated in Figure 12 between flap angles of 45° and 90° is visible
and expected with the sun elevation in November in France.
Figure 11.
Photos of the Stegos ‘glazing’ configuration on the test box with claps positioned as solar
caps and opened to a 90◦angle. Camera fixed on the roof wall of the test box.
The difference illustrated in Figure 12 between flap angles of 45
◦
and 90
◦
is visible and
expected with the sun elevation in November in France.
Energies 2022, 15, x FOR PEER REVIEW 13 of 18
(a) (b)
Figure 12. Light and shadow projection on the floor of the test box at different hours of the day for
two opening angles of flaps: (a) angle at 45° on November 12, and (b) angle at 90° on November 16.
Blue light at the end of the day is due to more diffuse illumination than the rest of the day.
3.5. Discussion
The measurements performed on the ‘opaque’ configuration do not provide direct
conclusions on the Stegos performance and its impact on a controlled volume as the test
box. While useful for the characterization using geometrical and thermal models, difficul-
ties in comparing different sets between each other are arguments to perform, in the near
future, with new experimentations with the following modifications:
• Addition of insulation on the tested façade for more impact on the whole test box
behavior;
• Coating of the aluminum plate with a black matte paint to reduce reflection induced
by the high reflectivity of aluminum and thus increase incoming heat flows. This
should help to compare different sets;
• Switch flaps coated with the blue, thermochromic paint for white- and black-painted
flaps to compare the results with extreme colors and determine the contribution of
the adaptive paint on the Stegos performance.
4. Towards Characterization through the Calibration of Grey Box Models
To face practical production challenges and collect feedback on bioinspired practice,
the authors experimented with design processes through the prototyping of the Stegos
system and the creation and use of a test bench. Several measurement campaigns (de-
scribed in Part 3) provided a first assessment of the system and guidelines for improved
measurements. However, intricate physical phenomena, including radiative, convective,
and conductive transfers, are still to be described to define better alternatives of the con-
cept in regards to the pursued functionalities. For this, a coupling between parametric
geometric models and heat transfer models is proposed and described in the following
sections.
4.1. Geometric Parametric Design
A geometrical model of the prototype integrated into the test box was created under
Rhinoceros Grasshopper. Geometrical parameters, either related to the Stegos or to the
general set (orientation, weather, and date), were defined as variables to be tested and
compared with regard to various indicators related to air, light, and heat regulation func-
tionalities, as displayed in Figure 13.
Figure 12.
Light and shadow projection on the floor of the test box at different hours of the day for
two opening angles of flaps: (
a
) angle at 45
◦
on November 12, and (
b
) angle at 90
◦
on November 16.
Blue light at the end of the day is due to more diffuse illumination than the rest of the day.
3.5. Discussion
The measurements performed on the ‘opaque’ configuration do not provide direct
conclusions on the Stegos performance and its impact on a controlled volume as the test box.
While useful for the characterization using geometrical and thermal models, difficulties in
comparing different sets between each other are arguments to perform, in the near future,
with new experimentations with the following modifications:
•
Addition of insulation on the tested façade for more impact on the whole test box
behavior;
•
Coating of the aluminum plate with a black matte paint to reduce reflection induced by
the high reflectivity of aluminum and thus increase incoming heat flows.
This should
help to compare different sets;
•
Switch flaps coated with the blue, thermochromic paint for white- and black-painted
flaps to compare the results with extreme colors and determine the contribution of the
adaptive paint on the Stegos performance.

Energies 2022,15, 891 14 of 19
4. Towards Characterization through the Calibration of Grey Box Models
To face practical production challenges and collect feedback on bioinspired practice,
the authors experimented with design processes through the prototyping of the Stegos
system and the creation and use of a test bench. Several measurement campaigns (de-
scribed in Part 3) provided a first assessment of the system and guidelines for improved
measurements. However, intricate physical phenomena, including radiative, convective,
and conductive transfers, are still to be described to define better alternatives of the concept
in regards to the pursued functionalities. For this, a coupling between parametric geometric
models and heat transfer models is proposed and described in the following sections.
4.1. Geometric Parametric Design
A geometrical model of the prototype integrated into the test box was created un-
der Rhinoceros Grasshopper. Geometrical parameters, either related to the Stegos or to
the general set (orientation, weather, and date), were defined as variables to be tested
and compared with regard to various indicators related to air, light, and heat regulation
functionalities, as displayed in Figure 13.
Energies 2022, 15, x FOR PEER REVIEW 14 of 18
Figure 13. Steps followed during the geometric modeling of the Stegos design implemented in the
test box: (from left to right) definitions of parameters, implementation in Rhinoceros Grasshopper,
use of embedded models, and evaluation according to various criteria.
In the ‘glazing’ configuration, the Stegos acts as a solar shading device and thus as a
light-management system. The objective here is to validate the geometrical representation
through Rhinoceros Grasshopper. For this purpose, a daylight analysis was performed on
a southern-fixed orientation, located in Bordeaux (France), and with dates set as the dates
of the experiments described in Part 3. The angles of the flaps varied from 0 to 90° and
were positioned horizontally. A comparison between the simulation on Grasshopper and
photographs of the experiments illustrated in Figure 14 shows very similar light projec-
tions. It is important to note that this comparison can only be qualified as qualitative, as
the authors do not provide numerical analysis of the photographs and because of inevita-
ble distortions due to perspective.
(a) (b)
Figure 14. Comparisons between simulations on Rhinoceros Grasshopper and photographs of
Stegos in solar cap configuration. (a) Comparison of the vertical shadow for an angle of 90°. Date:
Figure 13.
Steps followed during the geometric modeling of the Stegos design implemented in the
test box: (from left to right) definitions of parameters, implementation in Rhinoceros Grasshopper,
use of embedded models, and evaluation according to various criteria.
In the ‘glazing’ configuration, the Stegos acts as a solar shading device and thus as a
light-management system. The objective here is to validate the geometrical representation
through Rhinoceros Grasshopper. For this purpose, a daylight analysis was performed on
a southern-fixed orientation, located in Bordeaux (France), and with dates set as the dates
of the experiments described in Part 3. The angles of the flaps varied from 0 to 90
◦
and
were positioned horizontally. A comparison between the simulation on Grasshopper and
photographs of the experiments illustrated in Figure 14 shows very similar light projections.
It is important to note that this comparison can only be qualified as qualitative, as the
authors do not provide numerical analysis of the photographs and because of inevitable
distortions due to perspective.

Energies 2022,15, 891 15 of 19
Energies 2022, 15, x FOR PEER REVIEW 14 of 18
Figure 13. Steps followed during the geometric modeling of the Stegos design implemented in the
test box: (from left to right) definitions of parameters, implementation in Rhinoceros Grasshopper,
use of embedded models, and evaluation according to various criteria.
In the ‘glazing’ configuration, the Stegos acts as a solar shading device and thus as a
light-management system. The objective here is to validate the geometrical representation
through Rhinoceros Grasshopper. For this purpose, a daylight analysis was performed on
a southern-fixed orientation, located in Bordeaux (France), and with dates set as the dates
of the experiments described in Part 3. The angles of the flaps varied from 0 to 90° and
were positioned horizontally. A comparison between the simulation on Grasshopper and
photographs of the experiments illustrated in Figure 14 shows very similar light projec-
tions. It is important to note that this comparison can only be qualified as qualitative, as
the authors do not provide numerical analysis of the photographs and because of inevita-
ble distortions due to perspective.
(a) (b)
Figure 14. Comparisons between simulations on Rhinoceros Grasshopper and photographs of
Stegos in solar cap configuration. (a) Comparison of the vertical shadow for an angle of 90°. Date:
Figure 14.
Comparisons between simulations on Rhinoceros Grasshopper and photographs of
Stegos in solar cap configuration. (
a
) Comparison of the vertical shadow for an angle of 90
◦
. Date:
27 October 12:00
. (
b
) Comparison of the horizontal shadow on the floor of the test box for an angle of
90◦. Date: 19 November 15:00.
The results of these simulations alone are not sufficient to provide satisfactory de-
sign configuration in regards to light regulation in the ‘glazing’ scenario. To be vali-
dated,
they would
require the use of other criteria—for instance, daylight or glare analysis
showing adequate lighting in the enclosure during winter. In this sense, multi-objective
optimization would be adequate.
Nevertheless, a comparison of the simulations with measured projections validates
the geometrical modeling, and it can provide valuable inputs to better detail the external
boundary conditions in a heat-transfer model. We define two parameters, the horizontally
projected shadow g
floor,Stegos
and the vertically projected shadow
τStegos
on the tested
façade. Those can be simulated and be inputs of the ‘glazing’ and ‘opaque’ façade thermal
model, respectively:
gfloor,stegos =1−Sfloor,shade
Sfloor,tot
(1)
τStegos =1−
SStegos,shade
SStegos,tot
(2)
with S
floor,shade
indicating the shaded surface on the test box floor, S
floor,tot
indicating the
total surface area of the test box floor, S
Stegos,shade
indicating the shaded surface on the
Stegos, and SStegos,tot indicating the total surface area of the tested façade (Figure 15).

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Energies 2022, 15, x FOR PEER REVIEW 15 of 18
October 27, 12:00. (b) Comparison of the horizontal shadow on the floor of the test box for an angle
of 90°. Date: November 19, 15:00.
The results of these simulations alone are not sufficient to provide satisfactory design
configuration in regards to light regulation in the ‘glazing’ scenario. To be validated, they
would require the use of other criteria—for instance, daylight or glare analysis showing
adequate lighting in the enclosure during winter. In this sense, multi-objective optimiza-
tion would be adequate.
Nevertheless, a comparison of the simulations with measured projections validates
the geometrical modeling, and it can provide valuable inputs to better detail the external
boundary conditions in a heat-transfer model. We define two parameters, the horizontally
projected shadow g
floor,Stegos
and the vertically projected shadow τ
Stegos
on the tested façade.
Those can be simulated and be inputs of the ‘glazing’ and ‘opaque’ façade thermal model,
respectively:
g, 1
S,
S,
(1)
τ 1
S,
S,
(2)
with S
floor,shade
indicating the shaded surface on the test box floor, S
floor,tot
indicating the total
surface area of the test box floor, S
Stegos,shade
indicating the shaded surface on the Stegos,
and S
Stegos,tot
indicating the total surface area of the tested façade (Figure 15).
(a) (b)
Figure 15. (a) The shaded surface on the Stegos is the sum of all S
Stegos_shade_i
. (b) Simulated τ
Stegos
for
the 1
November (data for location: Bordeaux, France).
The Rhinoceros Grasshopper model was used to calculate one value of the τ
Stegos
,
needing 30 s computational time on a regular office computer.
4.2. Heat-Transfer Models: Grey-Box Approach Proposal
The complexity of the physical phenomena taking place in the Stegos integrated into
the test box prevents proposing a fully descriptive model. An alternative is to use partial
theoretical models coupled with data from performed measurements (Part 2), known as
the grey-box approach.
An RC (resistance, capacitance) model is proposed and represented in Figure 16. The
following hypotheses and simplifications are considered:
• The tested façade, including Stegos, is considered as a semi-infinite environment,
meaning that it is extending to infinity in all three directions, but only on one side of
a plane, here, the external environment.
• Only one layer of aluminum is included in the model; the 4 mm support frame is
perforated with hexagonal holes and can thus be neglected.
Figure 15.
(
a
) The shaded surface on the Stegos is the sum of all S
Stegos_shade_i
. (
b
) Simulated
τStegos
for the 1 November (data for location: Bordeaux, France).
The Rhinoceros Grasshopper model was used to calculate one value of the
τStegos
,
needing 30 s computational time on a regular office computer.
4.2. Heat-Transfer Models: Grey-Box Approach Proposal
The complexity of the physical phenomena taking place in the Stegos integrated into
the test box prevents proposing a fully descriptive model. An alternative is to use partial
theoretical models coupled with data from performed measurements (Part 2), known as
the grey-box approach.
An RC (resistance, capacitance) model is proposed and represented in Figure 16.
The following hypotheses and simplifications are considered:
•
The tested façade, including Stegos, is considered as a semi-infinite environment,
meaning that it is extending to infinity in all three directions, but only on one side of a
plane, here, the external environment.
•
Only one layer of aluminum is included in the model; the 4 mm support frame is
perforated with hexagonal holes and can thus be neglected.
•
The heat transfers are considered in one dimension, with internal boundary conditions
based on the internal air temperature and a fixed convective coefficient. Additionally,
the external boundary condition is given by the weather measurement.
•
The proposed model includes conductive, convective, and longwave radiative heat
transfers between the outside surface of Stegos (the aluminum plate) and the external
environment in a single thermal resistance.
•
The incident solar radiation is taken into account in two ways. The first contribution is
expressed as direct and diffuse radiation on the external surface of the aluminum plate
using the projected shadow ratio calculated with geometrical models (see
Part 3.1
).
A second contribution is provided through a factor f
Stegos
, which represents a solar
intake in the Stegos through the flaps.

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Energies 2022, 15, x FOR PEER REVIEW 16 of 18
• The heat transfers are considered in one dimension, with internal boundary condi-
tions based on the internal air temperature and a fixed convective coefficient. Addi-
tionally, the external boundary condition is given by the weather measurement.
• The proposed model includes conductive, convective, and longwave radiative heat
transfers between the outside surface of Stegos (the aluminum plate) and the external
environment in a single thermal resistance.
• The incident solar radiation is taken into account in two ways. The first contribution
is expressed as direct and diffuse radiation on the external surface of the aluminum
plate using the projected shadow ratio calculated with geometrical models (see Part
3.1). A second contribution is provided through a factor f
Stegos
, which represents a
solar intake in the Stegos through the flaps.
Figure 16. RC model of the wall assembly (case of ‘opaque wall’ configuration) with C
i
thermal
capacities and R
i
thermal resistances of the nodes.
5. Conclusions and Prospects
In this paper, we presented an envelope design derived from a bioinspired frame-
work. The system is a deformable and deployable skin, which can be positioned in front
of an opaque wall, as a glazing, or as the envelope itself. According to the configuration,
it can manage multiple regulation factors, such as heat, light, and air. Moreover, the de-
ployable elements are coated with an adaptive paint, in which the absorption coefficient
changes with the surface temperature.
A non-deformable but deployable version was prototyped and integrated into an ori-
enTable 1 m
3
insulated box as a test bench. Measurements of heat and light transfers were
performed for the opaque and glazing configurations. Limitations were identified in the
experimental protocols owing to the high reflectivity of the internal aluminum layer lim-
iting the solar gains, and as such, mitigating the impact of Stegos as a solar-shading de-
vice. This layer will be painted in black, resulting in higher heat transfers and allowing
better identification of the impact of each parameter.
The proposed bioinspired design methodology was experimented with at the begin-
ning of the project and resulted in the Stegos design. Feedback from this experience allows
it to further improve its implementation, especially with the additional data.
Future work includes the implementation of the ‘envelope’ configuration in the test
bench to perform measurements of thermal, light, and air transfers. A deformable version
of the concept is also planned to be prototyped and tested as well.
A follow-up of this project will be a generic methodology for the characterization of
dynamic envelope elements, such as a Stegos prototype based on the calibration of a
model against measurements on similar protocols. The introduced parameters R
Stegos
and
f
stegos
of the proposed RC model characterize the impact of Stegos on the opaque wall, but
Figure 16.
RC model of the wall assembly (case of ‘opaque wall’ configuration) with C
i
thermal
capacities and Rithermal resistances of the nodes.
5. Conclusions and Prospects
In this paper, we presented an envelope design derived from a bioinspired framework.
The system is a deformable and deployable skin, which can be positioned in front of an
opaque wall, as a glazing, or as the envelope itself. According to the configuration, it can
manage multiple regulation factors, such as heat, light, and air. Moreover, the deployable
elements are coated with an adaptive paint, in which the absorption coefficient changes
with the surface temperature.
A non-deformable but deployable version was prototyped and integrated into an
orienTable 1 m
3
insulated box as a test bench. Measurements of heat and light transfers
were performed for the opaque and glazing configurations. Limitations were identified in
the experimental protocols owing to the high reflectivity of the internal aluminum layer
limiting the solar gains, and as such, mitigating the impact of Stegos as a solar-shading
device. This layer will be painted in black, resulting in higher heat transfers and allowing
better identification of the impact of each parameter.
The proposed bioinspired design methodology was experimented with at the begin-
ning of the project and resulted in the Stegos design. Feedback from this experience allows
it to further improve its implementation, especially with the additional data.
Future work includes the implementation of the ‘envelope’ configuration in the test
bench to perform measurements of thermal, light, and air transfers. A deformable version
of the concept is also planned to be prototyped and tested as well.
A follow-up of this project will be a generic methodology for the characterization of
dynamic envelope elements, such as a Stegos prototype based on the calibration of a model
against measurements on similar protocols. The introduced parameters R
Stegos
and f
stegos
of the proposed RC model characterize the impact of Stegos on the opaque wall, but they
are not fully descriptive. We will use optimization methods to identify those parameters
in this generic grey-box model and stochastic methods using pseudo aleatory exploration
processes. Once calibrated, the model can be applied to design new, more efficient versions
of Stegos, and it will offer the opportunity to numerically integrate such an innovative
envelope element in thermal buildings’ simulation platforms to evaluate its global impact
on different buildings.
Author Contributions:
Conceptualization, T.H., A.D., T.V.W., F.A. and D.B.; methodology, T.H., A.D.,
T.V.W., F.A. and D.B.; validation, D.B. and F.A.; data curation, T.H.; energy models, T.H. and A.D.;
writing—original draft preparation, T.H.; writing—review and editing, T.H., A.D., T.V.W., F.A. and
D.B. All authors have read and agreed to the published version of the manuscript.

Energies 2022,15, 891 18 of 19
Funding:
This research was carried in the frame of the BIOINSPIRED project, funded by the Regional
Committee of Nouvelle Aquitaine (CNRA) and the Investments for the Future Program (PIA).
Data Availability Statement:
Publicly available datasets were analyzed in this study. The data can
be found at https://doi.org/10.5281/zenodo.5762420 (accessed on 21 January 2022).
Acknowledgments:
Additional help came from Damien Decker for the prototyping and measure-
ments, Saeed Kamali for the illustrations, and Myriame Ali-Oualla and Kaïs Bhouri for contributing
to the Stegos concept. The authors thank them.
Conflicts of Interest: The authors declare no conflict of interest.
Nomenclature
T Temperature (◦C) or (K)
HF Heat flux (W/m2)
S Surface (m2)
A Absorption coefficient (-)
R Reflectance (-)
τSolar transmission coefficient (-)
λThermal conductivity (W/m·K)
R Thermal resistance (K/W)
h Transmitted heat coefficient (W/K)
C Heat capacity (J/K)
G Normal direct and diffuse solar radiation (W/m2)
Abbreviations
ABS Acrylonitrile butadiene styrene
OSB Oriented strand board
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