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Proceedings of the International Association for Shell and Spatial Structures (IASS)
Symposium 2015, Amsterdam
Future Visions
17 - 20 August 2015, Amsterdam, The Netherlands
foldKITE: An Ultra-Lightweight Folded Structure
Pierluigi D’ACUNTO*, Juan José CASTELLONa, Alessandro TELLINIa, Shibo RENb
* a ETH Zürich – DARCH
Stefano-Franscini-Platz 5, 8093 Zürich (CH)
dacunto@arch.ethz.ch
b Arup Amsterdam
Abstract
The use of folding in design allows for the production of efficient structures capable to resist the
external applied loads by form; additionally, folding is an effective way to generate forms that can
address diverse spatial necessities. Developed as an entry to the IASS Expo 2015 out of a
collaboration between the Chair of Structural Design at ETH Zürich, the Rapid Architectural
Prototyping Laboratory (Raplab) at ETH Zürich and Arup Amsterdam, the project foldKITE aims to
explore the potentials of folded-plate systems in the field of ultra-lightweight structures.
foldKITE consists in a suspended structure with overall dimensions of 5.0m x 1.5m x 1.25m. Inspired
by the aviation sector, the geometry of foldKITE has been generated using a novel design method for
the integration of structural folding in architecture that is based on a three-dimensional design process
grounded on simple geometric operations. Following the design method, a surface has been virtually
folded within a predesigned tetrahedral grid, thus generating a folded-plate system that, due to its
inherent properties, also performs structurally. In fact, thanks to the utilization of a tetrahedral grid, it
is possible to activate within the folded surface a load-bearing system that is equivalent to a pin-
jointed three-dimensional truss where the folded edges represent the rods of the truss, loaded either in
tension or compression, and the vertices correspond to the hinged nodes. By additionally pre-stressing
the folded surface, a structural system working similarly to a stressed skin can be deployed.
The materialization of the full scale prototype of foldKITE has taken advantage of the use of ultra-
lightweight materials as well as of the construction techniques employed in the kite industry.
Specifically, the plates of the folded surface have been produced using a polycarbonate film with
polyester strands and they have been reinforced along the edges with 1mm-thick paperboard elements
mounted directly onto the fabric. The plates have been shipped to the site as individual elements and
then assembled at the Muziekgebouw in Amsterdam using a flap-to-flap connection system. Thanks to
the employment of ultra-lightweight materials, the total mass of foldKITE does not exceed 8.0 kg,
giving the structure the appearance to float in the air.
Keywords: IASS Expo 2015, folding, folded-plate system, suspended structure, ultra-lightweight,
kite, tetrahedral grid, graphic statics, polycarbonate fabric, stressed skin
Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2015, Amsterdam
Future Visions
1. Introduction
The occasion to participate in the International Association for Shell and Spatial Structures (IASS)
Expo 2015 in Amsterdam, gave the Chair of Structural Design together with the Rapid Architectural
Prototyping Laboratory (Raplab) at the Swiss Federal Institute of Technology (ETH) Zürich the
opportunity to establish a collaboration with Arup Amsterdam to investigate the potentials of the use
of folding in the field of structural design; this partnership resulted in the design of the suspended
folded structure foldKITE (Figure 1). The project has been specifically developed to address the
requests of the organizers of the IASS Expo 2015 to promote innovative structures that convey a
future vision on structural design.
Generally speaking, folded structures can be regarded as strong structures (Schnetzer et al.[7]) since
they do not undertake their load-bearing function in the background as hidden skeletons, but on the
contrary they convert the structural necessities into an opportunity for space making. In the project
foldKITE, the focus has been specifically put into the investigation of the relationship between load-
bearing capacity and space making potential, thus regarding the proposed design as a strong structure.
In architecture and structural design, one of the most effective employments of folding is represented
by folded-plate systems. These are generated by combining rigid plates to produce kinematically
stable folded geometries, which are able to resist the external applied loads by form. The series of
folded roofs designed by the Italian engineer Sergio Musmeci at the end of the 1950s can be regarded
as one of the most outstanding precedents of these systems in the field of structural design (Musmeci
[4]). In the architectural domain, a particularly remarkable example of the use of folded-plates is
represented by the project Capilla en Valleaceron (1997-2000) by Juan Carlos Sancho and Sol
Madridejos where the architects thoroughly investigated the spatial opportunities of folding as a
method for space making (Sancho and Madridejos [6]). It is taking these precedents as a reference that
the design of foldKITE has been developed. On the one hand, the goal of the project is to show how
folding can be employed to achieve structural integrity while introducing spatial differentiation within
a coherent formal system. On the other hand, the aim is to explore the boundaries of application of
folded-plate systems in the field of ultra-lightweight structures.
Figure 1: Overall View of the Suspended Structure foldKITE
Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2015, Amsterdam
Future Visions
2. Design Process
As an entry to the IASS Expo 2015, foldKITE had to comply with the regulation introduced by the
organizers of the exhibition. Specifically, the structure had to be designed in a way that its constituent
parts could be prefabricated off-site and transported to the site, the Muziekgebouw in Amsterdam,
using no more than six boxes in total, each with maximum dimensions of 1.00m x 0.75m x 0.65m and
a mass lower than 32kg; moreover, once built, the structure had to fit into an assigned virtual
bounding box of maximum dimensions of 8.00m x 4.00m x 4.00m and be able to be suspended from
the ceiling by means of no more than three cables.
Given these guidelines, a design concept has been put forward to challenge the aforementioned rules
with the introduction of even more radical restraints. With the intention of reducing the mass of the
system to the minimum, the number of boxes allowed for the transportation of the parts to the site has
been decreased from six to one. In addition, the number of suspension cables has been reduced from
three to one. As such, foldKITE has been conceived as an ultra-lightweight structure that is suspended
from the ceiling by means of one cable only, which should be inevitably aligned to the centre of mass
of the system and allow the structure to rotate around it. In order to consistently address these design
constraints and to pursue the idea of establishing a direct relationship between form and flow of the
inner forces, folding has been introduced as the main driver of the design.
In a first step of the design process, the global geometry of the structure has been generated using a
novel design method for the integration of structural folding in architecture (D’Acunto and Castellón
[2]) in the form of a spatial folded-plate system. Based on this global geometry, in a second phase
detailed solutions have been developed for the individual plates that constituted the folded geometry,
taking into account specific structural, manufacturing and transportation constraints.
2.1. Generation of the Global Geometry
The design of the global geometry of foldKITE has been inspired by multiple references in the
aviation sector. In particular, the idea has been followed to create a lightweight structure with high
sculptural qualities that at the same time appears to float in the air. The design method employed for
the development of the global geometry of foldKITE is based on a three-dimensional process
grounded on simple geometric operations (D’Acunto and Castellón [2]). The method allowed for the
generation of a triangulated folded-plate geometry in the form of a free-form folded surface while
providing, at the same time, the possibility to evaluate the structural properties of the system such as
its global stability and the magnitude of the internal forces. In this way, it has been possible to respond
to spatial and structural questions at once. Thanks to the use of a series of customized parametric
tools, the design method has been implemented within a digital environment, namely the three-
dimensional software McNeel Rhinoceros 3D® and Grasshopper®; by allowing for an interactive
way of designing, the parametric tools have facilitated the execution of the design operations while
giving the possibility to test easily different design solutions. In parallel to the digital exploration,
various physical models at 1:10 and 1:5 scales have been produced that, complementary to the digital
ones, gave the chance to assess intuitively the consistency of the different design proposals. The
design method includes four main operations: (A) Grid Generation; (B) Virtual Folding; (C)
Geometry Manipulation and (D) Structural Evaluation. After a complete first execution of the
process, the individual operations have been repeated in a non-linear sequence according to the
specific spatial and structural requirements.
Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2015, Amsterdam
Future Visions
Figure 2: Design Method Used for the Generation of the Global Geometry of foldKITE
2.1.1. (A) Grid Generation
Through Operation A, a space-filling non-regular tetrahedral grid has been generated in order to
define a spatial reference for the design of the geometry of foldKITE (Figure 2A). With this operation,
the overall topology of foldKITE has been outlined by setting the number of tetrahedra to be included
in the grid and their reciprocal connectivity. To keep the geometry of foldKITE relatively neat, a
rather simple configuration for the grid has been introduced that included 20 tetrahedra arranged along
a linear chain. It is thanks to the use of a tetrahedral grid and the possibility to activate both bar-and-
node action and plate action (Wester [8]) that the folded surface, which has been subsequently created
with the following operation, could achieve its global kinematic stability.
Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2015, Amsterdam
Future Visions
2.1.2. (B) Virtual Folding
Using the previously generated grid as a reference, with Operation B the global geometry of foldKITE
has been delineated by virtually folding a continuous free-form surface into the grid (Figure 2B), thus
producing a triangulated folded-plate system. With Operation B the overall geometrical properties of
foldKITE have been defined, such as the organization of the enclosed space and the number and
position of openings on the folded surface. In order to emphasize the continuity of the folded
geometry and to keep visual connectivity between the inside and the outside of the structure, the
folded surface has been created in a way that it continuously folds from the outside to the inside and
vice-versa, while self-intersecting in places. A specific tool has been employed here that automatically
generates a univocal topological diagram of the system. In particular, a consistent numbering logic has
been used to identify unambiguously every face and edge within the folded surface, as well as to map
their reciprocal connectivity.
2.1.3. (C) Geometry Manipulation
With Operation C, the position of the individual vertices of the tetrahedral grid has been adjusted in
space to shape the geometry of foldKITE (Figure 2C) according to the specific design intentions. In
this way, Operation C provided the opportunity to introduce spatial differentiation while keeping the
continuity of the form of the folded surface. Through this operation, various design solutions have
been investigated that were based on the same topological configuration, as defined with the previous
operations. It is with Operation C that the geometric constraints introduced by the aforementioned
rules could be directly addressed into the design process as external boundary conditions. As such, in
this first design iteration the overall size of foldKITE has been here limited to the assigned bounding
box of 8.00m x 4.00m x 4.00m.
2.1.4. (D) Structural evaluation
Through Operation D the correlation between the internal flow of forces of the previously generated
folded surface and its global form has been made explicit (Figure 2D). By designing within a
tetrahedral grid, the structural behaviour of the folded surface can be represented by a pin-jointed
spatial truss (Kotnik and D’Acunto [3]), where the vertices of each triangular plate correspond to the
hinged nodes and the edges to the bars, loaded either in tension or compression. Being foldKITE
meant to be suspended indoor, self-weight has been the only load case taken into consideration for the
structural evaluation; in particular, the mass of each triangular plate has been regarded as redistributed
to the corresponding vertices in the form of lumped masses by local bending action in the plane of the
plates (Wester [9]). Following the lower-bound theorem of Plasticity Theory (Muttoni et al. [5]) the
load bearing capacity of the system has been evaluated, considering in a first instance the structure as
a rigid-perfectly plastic system. This has been performed with graphic statics (Cremona [1]) which
allowed for the relationship between form and inner forces to be explicitly shown, hence working as
an operative structural diagram (Kotnik and D’Acunto [3]). Operation D gave the chance to address
directly specific structural question and modify the geometry of the folded surface accordingly. For
example, in order to avoid buckling within the folded geometry, the latter has been adjusted to exclude
compression forces on the free edges or by reducing their free length. Moreover, to improve the
general stability of the structure, the folding angles between the plates have been increased or reduced
according to the intensity of the inner forces.
Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2015, Amsterdam
Future Visions
2.2. Evolution of the Design Solution
Following the previously described design method, the first proposal for the global geometry of
foldKITE resulted in an asymmetric structure of 5.0m x 2.0m x 1.5m in size and constituted by 49
triangular plates of various dimensions (Figure 3A). In order for this solution to comply with the
aforementioned constraint according to which the entire structure had to fit within a container of
1.00m x 0.75m x 0.65m and considering the size limitation of the available manufacturing
machineries, most of the plates would have had necessarily to be split into sub-parts. Due to the
disadvantages of this procedure, also in terms of reduced structural performance for the presence of
extra inner joints within the plates, an alternative design solution has been searched for to keep the
individual plates as unique pieces.
Hence, a second iteration of the design process has been run, this time introducing the dimensions of
the container as an external boundary condition in the first place. With Operation A (Grid
Generation), the initial tetrahedral grid composed of 20 tetrahedra has been re-subdivided into 40
tetrahedra; while keeping a global geometrical configuration similar to the one of the previous design
proposal, with Operation C (Geometry Manipulation) the vertices of the tetrahedral grid have been
adjusted in order to constrain the size of each plate to fit the one of the container. As a result, a second
design proposal based on 85 triangular plates has been generated (Figure 3B). Although it avoided the
plates to be split into smaller parts, this new solution relied on a relatively high number of plates to be
built: a drawback that would have increased the manufacturing time as well as reduced the
construction efficiency in comparison to the first proposal.
A new global geometry of foldKITE has been then developed that combined the advantages of both
first and second proposal. In particular, using the latter as a starting point, a longitudinal axis of
symmetry has been introduced to simplify the overall complexity of the system, yet without
compromising its sculptural quality. After iterating the design process for a third time, the final
solution resulted in a geometry composed of 65 triangular plates and 100 independent edges, with
overall dimensions of 5.0m x 1.5m x 1.25m (Figure 3C).
Figure 3: Evolution of the Design Solution
Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2015, Amsterdam
Future Visions
2.3. Detail Design
Based on the final proposal for the global geometry of foldKITE, a detail design has been initiated for
the development of the plates constituting the folded geometry. This phase has been mainly carried
out working on physical prototypes at 1:1 scale. If in the first phase of the design process the
materiality of the suspended structure has not been directly taken into account, in this second step of
detail design explicit questions related to materials and their properties have been addressed. Given
the initial intention of designing foldKITE as an ultra-lightweight structure, a thorough research on
lightweight materials have been conducted. Indeed, an important reference in this phase has been
found in the sport kite industry; the necessity to produce flying objects able to resist severe wind
conditions has pushed this sector to develop high-strength materials that are, at the same time, ultra-
lightweight. Because of its mechanical properties and its ethereal and translucent materiality that fitted
particularly well with the design concept, the hydrophobic kite fabric Icarex® (PC-31) has been
selected as the main material for the production of the triangular plates of foldKITE. Specifically, this
kite fabric is a polycarbonate film reinforced with polyester strands with an area density of 31g/m2.
In compliance with the previously described structural model for folding, according to which the main
inner forces in a folded geometry travel along the folded edges, a strategy has been put forward to
reinforce the kite fabric along these edges with fiberglass strips; the latter could be directly laminated
onto one side of the PC-31 fabric using two-component epoxy resin, thus generating rigid triangular
frames. A physical prototype of a generic plate has been then developed as a test (Figure 4A).
Although the prototype showed an adequate degree of lightness and structural stability, due to
manufacturing limitations such as the impracticability to handle safely the epoxy resin and easily cut
the fiberglass strips, other solutions have been looked for. After testing various alternatives, frames
made of 1mm-thick solid bleached board (SBB) with an area density of 600g/m2 have been eventually
chosen to replace the fiberglass strips as the reinforcement of the edges of the triangular plates.
Contrary to the fiberglass strips, the SBB could be easily glued to the PC-31 fabric using common
multipurpose solvent-based spray adhesive. While satisfactory in relation to the structural
requirements, the employment of SBB also opened the possibility of using a digital cutter to cut the
individual frames at once.
In order to physically join the triangular plates to generate the folded surface, a solution based on a
flap-to-flap connection has been developed by adding folded flaps along the edges of the plates, thus
creating cylindrical-hinged connections. Other than providing a satisfactory solution for the joining of
the plates, the introduction of the folded flaps improved the local structural stability of the edges
against their own self-weight, while reducing their risk to buckle under high compressive normal
forces. Special attention has been paid to the fabrication of the flaps. To keep the manufacturing
process simple, a first design alternative has been evaluated where the flaps were cut at once together
with the frames and the SBB was scored on one side along the edges to generate the required
cylindrical hinge (Figure 4B); however, this solution had to be rejected soon after experiencing severe
problems of delamination of the SBB along the scored lines in those tests where the flaps were loaded
with local shear forces perpendicular to the axis of the scored lines. A definitive solution has been
found by taking as a reference the bookbinding sector and specifically the hardcover binding
technique that allowed for a robust yet neat connection system to be deployed; as such, unlike the
previous alternative, the flaps have been first cut as independent elements from the frames and
subsequently connected to them along their edges using 160g/m2 white paper strips with poly-vinyl
acetate (PVA) glue on one side and kite fabric with spray adhesive on the other (Figure 4C).
Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2015, Amsterdam
Future Visions
(A) Fiberglass Strips
(B) Flaps Connection Through Scoring
(C) Flaps Connection Through Binding
Figure 4: Detail Development of the Plates
3. Construction of the Suspended Structure
The fabrication of the plates of foldKITE has been carried out entirely off-site, taking advantage of the
use of the digital manufacturing machines of the Rapid Prototyping Architectural Laboratory (Raplab)
at ETH Zürich. The plates have been consequently arranged into a box of prescribed dimensions and
shipped to the Muziekgebouw in Amsterdam, where the final assembly and the rigging of the full
scale structure has taken place.
3.1. Manufacturing of the Plates
The manufacturing process of the plates has been organized in three main steps: cutting of the SBB
frames and flaps; mounting of the frame to the PC-31 kite fabric; connection of the flaps to the
frames.
The SBB frames and flaps have been cut out from 1.10m x 0.80m paperboards using a digital cutter
(Figure 5A). Based on the global geometry of foldKITE defined previously and according to the
solution deployed for the frames, a customized software has been employed to generate the cutting
pattern to be used to feed the digital cutter. In particular, thanks to the tool it has been possible to
adjust automatically the width of the individual sides of the frames to be proportional to the length of
the corresponding edges as well as to the intensity of the inner forces, as evaluated with the previously
introduced Operation D (Structural Evaluation). In addition, using the tool each flap has been labelled
with a univocal code representing the number of its corresponding edge in the global geometry as
produced with Operation B (Virtual Folding), along with the numbers of the plates directly connected
to it.
Before mounting the SBB frames to the PC-31 fabric (Figure 5B), the latter has been first laid out
onto a vacuum table; apart from facilitating the gluing operation, this also allowed for the fabric to be
perfectly stretched in order to avoid the presence of undesirable wrinkles. Furthermore, because of this
Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2015, Amsterdam
Future Visions
procedure, after the frames have been connected to the fabric a minimum level of pre-stressing could
be introduced into the plates, thus generating a structural system working similarly to a stressed skin.
The flaps have been connected to the frames following the previously described hardcover binding
technique (Figure 5C). In this phase, special attention has been paid in keeping an adequate spacing in
the joints between the flaps and the frames, for these connections to actually work as full cylindrical
hinges. Moreover, the water content of the PVA glue has been constantly monitored to avoid unsought
effects of soaking in the SBB.
Overall, for the manufacturing process 14.42m2 of PC-31 fabric has been employed along with 9.40m2
of SBB. The total mass of the system has then resulted in 7.15kg, well below the allowable maximum
mass prescribed by the regulation of the exhibition.
(A) Frames Cutting with Digital Cutter
(B) Frames Mounting on Vacuum Table
(C) Frames Binding
Figure 5: Manufacturing Process
3.2. Final Assembly and Installation On-Site
The final assembly of the full scale folded structure has been accomplished by joining the individual
plates through the previously described flap-to-flap connection. Thanks to the versatility of this
connection system, the assembly of the plates has been executed working entirely by hand and using
ordinary hand tools only. In particular, cyanoacrylate (CA) fast-acting adhesive with a shear strength
of 24 N/mm2 has been used to pair the corresponding flaps of adjacent plates together; for safety
reasons, 6.0mm and 8.0mm-wide metal staples have been also added to prevent possible unexpected
creep over time along the glued connections.
With the aim of keeping the construction process easily manageable, a clearly defined assembly
sequence has been followed. The sequence has been generated according to extensive assembly tests
carried out on 1:10, 1:2 and 1:1 prototypes of foldKITE. In fact, a strategy has been developed to erect
the structure based on four main sub-clusters (Figure 6) that have been initially built as independent
parts and then connected together. In particular, the possibility to assemble at first the sub-clusters in
Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2015, Amsterdam
Future Visions
their unfolded two-dimensional configuration and to fold them afterwards in three-dimensions has
allowed for the complexity of the system to be broken down and as such to facilitate the whole
erection process. That is, the three-dimensional complexity of the nodes of the structure emerged out
directly of the assembly process and no specific three-dimensional connector has been necessary for
the construction. Although the built structure proved to have an overall high level of stiffness,
ignoring the behaviour of the system on the long term, for safety reasons extra SBB reinforcement
have been placed around the openings where the local deformations under self-weight were higher.
After the entire folded structure has been completely built, the rigging construction necessary for the
connection of the suspension cable has been produced. A steel wire rope with diameter of 4.0mm in
conjunction with a cable gripper and a swivel have been employed to permit the free rotation of the
structure. To distribute the tensile stresses of the suspension cable evenly to the folded structure, three
secondary wire ropes with diameter of 2.0mm have been used to join the suspension cable to the
folded system; each of them has been in turn connected to the folded structure along three SBB flaps
using wire rope loops in combination with common carabiners, wire rope grips and aluminium crimp
sleeves.
The entire assembly process has been completed by the authors in around 10 working hours. Despite
of its dimensions, thanks to its extreme lightweight, foldKITE has been easily transported from the
assembly area to the site and eventually suspended from the ceiling of the Muziekgebouw at 4m from
the ground (Figure 7).
Figure 6: Assembly Logic
Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2015, Amsterdam
Future Visions
Figure 7: Lateral View of foldKITE in the Muziekgebouw (Amsterdam)
Figure 8: foldKITE in the Muziekgebouw (Amsterdam) Seen from Underneath
Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2015, Amsterdam
Future Visions
4. Conclusions
foldKITE emerged out of the negotiation between design, structural, manufacturing and transportation
constraints. Beside its overall formal simplicity, foldKITE underlines a high level of complexity. As a
three-dimensional structure based on a continuous yet differentiated folded surface, it is necessary to
move around it and look at it from different perspectives to understand it entirely. In fact, once on site
each side of foldKITE has a completely different presence, due to the different lighting conditions on
the individual folded plates; this is also emphasized by the rotation of the structure around the
suspension cable. It is especially the play of light and shadows on the folded geometry and its ethereal
materiality that lends the structure the appearance to float in the air (Figure 8). As a result, by pushing
the boundaries of folded-plate systems into the field of ultra-lightweight structures, the project has
shown how folding could be effectively employed to achieve structural integrity while introducing
spatial differentiation within a coherent formal system, thus promoting a possible future vision on
structural design.
Acknowledgement
Special thanks to the students Jonas Hodel and Leo Kleine for their help during the manufacturing
phase and to Prof. Dr. Joseph Schwartz for his support throughout the development of the project.
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