Modelling the form. Heinz Isler, Frei Otto and their approaches to form-finding

Full text

Giulia Boller and Joseph Schwartz
565
Modelling the form. Heinz Isler, Frei Otto and their approaches to
form-finding
Giulia Boller and Joseph Schwartz
Chair of Structural Design, Institute of Technology in Architecture (ITA)
1. Introduction
1.1 Finding and validating structural forms through physical models
In architecture, the definition of a form is an important step in the design process: it configures aesthetically and
spatially the intended proposal and it embodies an iterative process that determines a state of continuous change
[1], to reach the most suitable shape for a specific design problem. When architectural and structural features
come together, it is possible to achieve a reasonable design from different perspectives and the form represents
the vehicle through which this achievement is made possible. This is especially true for shell structures, that work
mainly under compression forces, as well as for pure tensile structures like nets. Since their shape follows
physical laws, the physical model plays a prominent role in design because it represents the most comprehensive
method by which it is possible to acquire knowledge [2]. It stands as the medium through which it is possible to
materialize in a first approximation the initial idea, to translate it into a realizable structure.
The physical model help both in the form-finding process and in the validation procedure of the conceptual idea.
In the first case, the designer subordinates himself to the supremacy of form [3]: he sets the conditions to make
the model finding the most appropriate shape for the defined problem. In this circumstance, the model stands as
the main actor in the design process, whereas the person studies the results coming from natural laws. Frei Otto is
considered one of the most important figures in this area of expertise.
When the initial design idea is defined, instead, the physical model helps its further development by validating its
form, through multiple iterations. The study of the forces under different load types contributes to evaluating the
shape, in equilibrium between structural and architectural considerations. Heinz Isler’s first contact with physical
models was in this direction: his professor Pierre Lardy and Hans Hauri at ETH Zürich [4] developed precise
statical models to control the elastic behaviour of specific structures, on the basis of Eduardo Torroja’s laboratory
in Madrid. His first individual contribution to the scientific community, though, was the paper “New Shapes for
Shells” in 1959 [5], that opened up a new perspective on form finding shell structures based on an experimental
approach to design.
1.2 Frei Otto: from intuition towards science
Through a methodology based on direct observation, Frei Otto used his experiments to discover forms not yet
realized, going beyond the ones definable by mathematics and looking more closely at natural phenomena. His

Modelling the form. Heinz Isler, Frei Otto and their approaches to form-finding
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broad curiosity in every self-forming process helped him in the design process by observing the physical laws
behind any experiment. In his work, the concept of form finding highlighted the importance of the scientific
research for the shape definition, that uses photography as a tool to study specific aspects of an event. Since the
processes observed in his experiments were constantly changing, he used images to capture the ephemeral
phenomenon and with them he further developed his methodology. Producing and collecting images [6], he
studied processes and derived data. Belonging to academia, he always looked for scientific value in his design
explorations, to define a more stable theory behind his physical models. His best-known experiments were made
with soap film by taking advantage of the physical law of the minimal surface as the smallest surface between the
border conditions, characterized by equal stresses.
Frei Otto founded the Institute for Lightweight Structures at the University of Stuttgart in 1961 and conceived its
building in 1964 as a way to explore the translation from the physical process of a soap film model to the
full-scale structure (Fig. 01). At the same time, the roof, a tent made of a polyester translucent membrane that sits
on a steel net, represents the full-scale prototype of a section for the German Pavilion of Montreal, built for the
Expo of 1967 [7]. The form of the element was found through the soap experiment, obtained by lifting a central
point of an ideal circular surface, to define an opening in the form of a drop.
Fig. 01
–
Frei Otto, Institute for Leightweight Structures, Stuttgart, 1964 [gta Archives, ETH Z
ü
rich]
The design showed Frei Otto’s novel approach to form finding. His method helped to define architectural as well
as structural concepts, with reference to physical laws. The found form for the pavilion was validated through an
analytical approach by Fritz Leonhardt and Wolfhardt Andrä. Since Otto’s German Pavilion appeared to be a
newly-found shape never constructed before, the design was also controlled by accurately measuring models that
tested specific load conditions on small-scale prototypes.

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1.3 Heinz Isler: defining shells through accuracy
In his IL publications, Frei Otto recognized Heinz Isler as the main contemporary reference for shell structures
based on pneumatic and hanging membranes as form finding methods [8]. On the other hand, Heinz Isler mainly
referred to his own work and in particular to the three categories for finding “new shapes for shells” through
physical models: “freely shaped hill”, “membrane under pressure” and “hanging cloth reversed” [9]. They were
based on natural laws, which were the main factors influencing the shape and the most suitable design solution
for the problem proposed. Isler communicated his work through the above-mentioned form finding categories.
His approach to form finding was referred to observations coming from daily life (the pillow, the hanging
membrane), transformed into devices for scientific thinking that ensured for him the correct understanding of the
chosen design. Even though simple, this intuition was supported by a precise structural understanding and was
confirmed by the number of built shells [10]: it represented his major contribution to the scientific community of
structural design, placing him already at the beginning of his career as an independent professional, with an
innovative approach to shell design.
Looking at the methodology adopted, the building for the company Sicli SA in Geneva (1969), designed by Heinz
Isler together with the architect Constantin Hilberer, is a paradigmatic example in this direction. Isler took it also
as a reference in the projects he did in collaboration with Frei Otto (see below). The building represents the most
complex free form shell ever designed by him, obtained through the form finding method of the hanging cloth
reversed and sitting on seven points. He produced fifteen different gypsum models of the chosen concept, to
identify the optimal shape through form finding [11] (Fig. 02).
Fig. 02
–
Heinz Isler, Hanging Membrane Model, Sicli SA, Geneva, 1968 [gta Archives, ETH Z
ü
rich]
For most of the gypsum models based on the hanging membrane principle, Heinz Isler and his collaborators
annotated the result of each test, highlighting the problems that needed to be improved in subsequent experiments
[12]. In this case, the shape was defined in collaboration with the architect as a rough concept and then validated
through form finding procedures that helped to define the final shape, informed structurally by the hanging
membrane principle. The form finding approach did not play the prominent role in the initial conceptual phase to
explore multiple different design possibilities, as in Frei Otto’s Institute in Stuttgart, but it is more the method
through which intuition is validated and optimized, to find the ideal shape, closest to the defined concept.

Modelling the form. Heinz Isler, Frei Otto and their approaches to form-finding
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2. Heinz Isler and Frei Otto: the collaborative projects
2.1 Different engineering cultures, similar results
Even though they had different approaches to form finding, Heinz Isler and Frei Otto worked on similar design
concepts in the Fifties and Sixties. The explorations developed for umbrella-shaped elements represent the most
evident point of contact in this direction: they refer to the simple experiment that uses a pre-stressed membrane
fixed along a continuous border, with a point load applied on its surface. Frei Otto had studied it already at the
time of his dissertation in 1954, where he pointed out its potential uses in the development of curved prestressed
membranes as roof elements [13]. This study was then applied to the temporary project for the
Bundesgartenschau in Kassel (1955), where he developed three mushroom-shaped elements as a shading system
[14]. More than ten years later, the same concept, but with different boundary conditions, was developed by
Heinz Isler in the unbuilt project Rive in Neuchatel (1968). The base module consisted of a stressed membrane
with a point load applied on its surface, attached to a steel squared frame, with a dimension of 12 metres on each
side [15]. The project was composed of multiple modules combined together, to produce a canopy for a
commercial centre. Even though the project was not realized, Isler produced a lot of physical models, to validate
the shape, that encapsulates some clear influences from contemporary projects of others, especially the
explorations of Frei Otto, with whom he also started working in the same period.
Fig. 03
–
Frei Otto, Prototype for the temporary exhibition at the Bundesgartneschau, Köln, 1969 [gta
Archives, ETH Z
ü
rich]

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In the form of reversed umbrella-shaped elements, Isler and Otto developed a shading system for the temporary
exhibition at the Bundesgartenschau in Köln (1969-1972).
In this case, though, their role in the project is clear: Frei Otto was responsible for the design concept and the
design development, including construction drawings and prototypes (Fig. 03), whereas Heinz Isler worked as
structural engineer, validating the chosen form and controlling it with specific measuring devices.
Their exchanges became much more fruitful in two other relevant projects: the Olympic Stadium in München
(1967-1972) and the station of Stuttgart 21 (1997-…), (see below).
2.2 Spanning over the design limits: between tension and compression
The project for the roof of the Olympic Stadium in München (1967-1972) brought together different scientific
cultures and approaches to structural design for the first time. Somehow, all the most eminent architects and
engineers of that period were involved in the process: there is a famous picture that proves this occasion, with
Fritz Auer, Rudolph Bergermann, Heinz Isler, Fritz Leonhardt, Frei Otto and Jörg Schlaich discussing one of the
physical models produced for the project (Fig. 04). For this reason, the event stands as the meeting point between
Frei Otto, Heinz Isler and their respective approaches to form, within the broader history of the development of
this innovative long span roof.
Fig. 04
–
Design Meeting, Olympic Stadium, from left: Gabriel, Bergermann, Leonhardt,Schlaich, Otto, Auer,
Isler, 1968 [G. Vrachliotis (Ed.), Frei Otto - Denken in Modellen, Leipzig: Spector Books, 2017, p. 46]

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The project competition took place in 1967 and the winning team was represented by the architectural office
Behnisch & Partner. Even if the main idea for the roof came from the one developed for the German Pavilion in
Montreal, which was at that time under construction, Frei Otto was not involved in the competition team. He just
acted as an external consultant for the definition of the form, advising on the feasibility of the design, together
with Fritz Leonhardt, the engineer for the Montreal Pavilion [16]. Heinz Isler, instead, was part of the competition
team, being responsible for the engineering validation and the constructability of the project. As reported in a note
written by the organizers in 1970, he contributed substantially to the development of the winning proposal [17].
The construction of the roof is based on a big surface that is hanging through a steel net, with a double curvature
that resists any load and which is produced by the tension among a system of anchorages at different heights.
Some of them are pylons, some others are cables that act as bracing elements.
The form of the steel net was found through the analogy with a soap film membrane, obtained by a geometric
system with comparable border conditions [18]. This form finding method was well known to Isler, since he cited
it in some publications, comparing it with his more usual pneumatic technique and highlighting the difficulty in
measuring such an ephemeral experiment [19]. Until now, though, there is no proof that he had ever used this
approach to find a new form for one of his design explorations. It seems plausible, then, that even in the project
for the München Stadium he did not explore the proposed solution with soap film form-finding models, but
simply limited his contribution to a correct structural understanding of the defined form, using more common
analytical calculations during the competition phase. At the same time, since Frei Otto took an active part in the
design development just after the end of the competition (Fig. 05), the form for the roof was probably defined
through analogy with the one under construction in Montreal, without specific form finding models during the
competition phase.
Fig. 05
–
Frei Otto, Physical Model of the tensile roof, 1968 [gta Archives, ETH Z
ü
rich]

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It is still not clear why Heinz Isler, who was famous in the engineering community for building concrete shells
under compression, was involved so actively in the initial design of a tensile lightweight roof. After the
competition phase, he was mainly asked to enhance the use of the measuring physical models, pushing the limits
of modelling techniques by developing accurate apparatuses in small-scale (Fig. 06).
Fig. 06
–
Heinz Isler, Validating model for the development of the tensile roof, Olympic Stadium, M
ü
nchen,
1968 [gta Archives, ETH Z
ü
rich]
Again, he acted then more as an engineer that validated the form proposed by others through his accurate
experimental approach, working closely with the physical models produced by Frei Otto, which were built in
different scales and for different purposes.
The interrupted professional collaboration between Frei Otto and Heinz Isler started again in the late Nineties,
with the project for the new station of Stuttgart 21. At this time discussions about form finding became more
prominent in their exchanges. Even if taking different roles, they were both involved in the definition of the
correct form for the chalice-shaped column supporting the station’s roof. The materials produced represent an
important contribution in the understanding of their experimental approach to form finding, within the broader
scientific community and at the turning point of the technical tools, between physical and digital models.
The project for the new station of the city of Stuttgart is among the most important infrastructure projects of the
last decades in Germany. The station is located underground, providing the city with a large green public space.
The lighting below is provided by 28 skylights which also work as the supporting elements for the roof. Through
their unusual shape, the load of the surface at the ground level is transferred to a relatively small point at the
station level, creating an opening with a diameter of 27 metres (Fig. 07).

Modelling the form. Heinz Isler, Frei Otto and their approaches to form-finding
572
Fig. 07
–
Ingenhoven, Overdiek, Kahlen and Partner, Winning proposal for the new station, Stuttgart 21, 1997
[gta Archives, ETH Z
ü
rich]
In the developed design, now under construction, the double curvature of the column works as a shell structure,
whereas the roof above has a plate behaviour. The winning team was represented by the architectural office
Ingenhoven, Overdiek, Kahlen and Partner. This time, Frei Otto was officially involved as the structural
consultant within the design team, especially for the form finding phase. The engineering support for the full
project was from Büro Happold and, in the second part of the competition phase, additionally by the office of
Leonhardt, Ändra and Partner. Heinz Isler, originally a member of the competition jury as a structural expert, was
then involved in the further design development and, for a short period, his presence influenced the discussion on
methodology, required to define the appropriate structural forms. Otto’s atelier in Berlin and Isler’s office in
Lyssachschachen were the two main locations where meetings regarding this discussion took place.
From different perspectives, Isler and Otto made experimental tests to reach the same designed shape, to define
the more suitable form for the supporting element. Having experience of soap film experiments, Otto started from
the drop shape already used for the München roof and the Montreal Pavillion.

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573
Fig. 08
–
Frei Otto, Soap Film Model for the development of the chalice-shaped column, Stuttgart 21, 1997
[gta Archives, ETH Z
ü
rich]
By reversing it, the form becomes fully under compression and can be thus conceived as a concrete shell (Fig.
08). Together with these experiments, Otto worked also on the concept of the hanging chain, in the form of a
polygonal mesh anchored at high and low points which, develops the appropriate geometry under its own weight,
[20] (Fig. 09).
Fig. 09
–
Frei Otto, Hanging Net Model for the development of the chalice-shaped column, Stuttgart 21, 1997
[gta Archives, ETH Z
ü
rich]

Modelling the form. Heinz Isler, Frei Otto and their approaches to form-finding
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On the other hand, Isler used physical models based on the hanging membrane principle. He constructed a
complex apparatus, hanging a rubber membrane on six points along the edge and fixing it at a central point on the
base, with a hole in the middle part (Fig. 10). Through it, he created two different gypsum models that he then
studied in the same way as in his previous free-form shell projects: geometric studies as well as rough structural
testing, before developing further more accurate measuring models.
Fig. 10
–
Heinz Isler, Hanging Membrane Model for the development of the chalice-shaped column, Stuttgart
21, 1997 [gta Archives, ETH Z
ü
rich]
Even though with similar results, the form found is not exactly the same in the two approaches (soap film and
hanging model), as Isler highlighted in one of his annotations [21]. Looking closer at the shape, it is evident that
the physics behind the two form finding methods is completely different: on the one hand the minimal surface
obtained by the soap film creates an equal tensional state on the entire surface, whereas the hanging membrane
defines the stress distribution according to its own weight. At the same time, there is difference between the
models made with a hanging fabric (Heinz Isler) and the ones with a hanging net (Frei Otto) [22]: in the first case
the stresses are distributed continuously on the surface, whereas on the other they follow the main distribution of
the net’s cables. On the basis of these considerations, it becomes clear that obtaining the same design using two
different form finding approaches is problematic. Even though the duo collaborated just for a short period of time,
their discussions still represented a fruitful contribution to the scientific community, debating on the topic:
“Which is the best form or even the correct form? This will be the crucial question” [23].

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3. Putting science into physical models: concluding remarks
Looking at the projects that were developed in collaboration between Heinz Isler and Frei Otto, the roles played
seem quite clear: most of the time the former did not work during the form finding phase, since he was
responsible for the structural calculations and validations, whereas the latter, being an architect, worked in the
design team, with main responsibilities for defining the form of the design. Their discussions about the different
form finding methods and their respective approaches were not so frequent during their collaborative period. A
lot of materials regarding measuring devices for more advanced phases of the design process were exchanged, but
in the Heinz Isler Archive at Eth Zürich no exchanges about form finding are recorded for the late Sixties, at the
time of the projects for the Olympic Stadium in München and the Bundesgartenschau in Köln. Even though for a
short period of time, the only occasion when they discussed their approaches to form finding is the design
development phase for the chalice-shaped column of Stuttgart 21. As pointed out in the previous paragraph,
though, they did not have such a long and productive exchange, specifically on form finding: each one continued
developing his own technique, with no influences from the other methods used, pointing out the differences in the
corresponding approaches.
From this perspective, it is possible to place the two figures within their contemporary scientific community with
a more stable understanding of their contribution. Frei Otto started his design explorations looking closely at
natural phenomena, analysing them through a scientific approach. Somehow, he put science into his form finding
methods and they helped him in the definition of the correct design solution for every proposed problem. Heinz
Isler, instead, used nature mainly as a formal reference. His form finding devices were much more related to a
traditional craftmanship that confined physical laws to an immediate understanding of structures and for this
reason, they were also powerful as a communicative tool, allowing him to present his shells through his physical
experiments. Acting as a consultant engineer in most of his collaborative projects, it seems that his most
recognized expertise at that time was in the development of complex measuring experimental devices, to validate
the proposed design. This recognition is quite different from the one for which he is well-known in the
engineering community today: he stands as the reference for an innovative experimental approach to shell design,
based on form finding models. As highlighted in the projects studied in this text, his scientific contribution seems
to be more related to validating experimental methods, through which he was able to confirm or correct the shape
designed by someone else, rather than to the form finding physical models. From this perspective, Heinz Isler’s
contribution to the free form shells that are considered his masterpieces needs to be examined more closely: if in
the cases analysed the form was mainly defined by the architect and Isler helped in its further definition and
validation, is it still possible to consider the form to be found purely through Isler’s form finding method,
subordinating the role of the architect involved in the design process? These questions arise in the broader
understanding of Heinz Isler’s contribution to the history of engineering and culture and open up a different
understanding of his work, with the focus on his physical models.
Acknowledgements
The authors would like to thank the students Severin Jann and Valentin Ribi for their work on the archive
materials of the project Stuttgart 21 at the Heinz Isler Archive, gta Archives, Eth Zürich.
References
[1] Cf. E. Schaur (Ed.), Grundlagen. Form, Force, Mass. IL 21, Stuttgart: Karl Krämer Verlag, 1979.
[2] Cf. S. Gaß, (Ed.). Experimente. Form, Force, Mass. IL 25. Stuttgart: Karl Krämer Verlag, 1990, pp. 1.2-1.9.

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[3] H. Isler, ‘Concrete Shells Derived from Experimental Shapes’, IABSE, vol. 4, no. 3, 1994, pp. 142–47.
[4] H. Isler, ‘Generating Shell Shapes by Physical Experiments’, Bulletin of the International Association for
Shell and Spatial Structures, vol. 34, no. 1, 1993, pp. 53–63.
[5] H. Isler, ‘New Shapes for Shells’, in Journal of the International Association for Shell and Spatial Structures,
1959, paper C-3.
[6] Cf. D. Fabricius, ‘Capturing the Incalculable. Frei Otto’s Experimental Models’ in S. Hildebrand and E.
Bergmann, (Eds.), Form-Finding, Form-Shaping, Designing Architecture, Mendrisio: Mendrisio Academy
Press, 2015, pp. 49-64.
[7] Cf. M. Balz, B. Burckhardt, L. Medlin, G. Minke and F. Otto, ‘Studie zum Ausbau des Versuchsbaus
Stuttgart-Vahingen’, document unpublished, 1966 (217-0180, gta Archives, ETH Zürich).
[8] Gaß, Experimente (Note 2), pp. 1.6-1.8
[9] H. Isler, ‘New Shapes for Shells’, in Journal of the International Association for Shell and Spatial Structures
(Note 5)
[10] Cf. H. Isler, ‘‘New Shapes for Shells’ - Twenty Years After’ in Journal of the International Association for
Shell and Spatial Structures, vol. 20, 1979, pp. 9-26
[11] S. C. Chuang and J. Chilton. 2016. ‘Design and Modelling of Heinz Isler’s Sicli Shell’ in K. Kawaguchi, M.
Ohsaki, and T. Takeuchi (Eds.), Proceedings of the IASS Annual Symposium “Spatial Structures in the 21st
Century”, Tokyo, 2016.
[12] Cf. Archival Materials 217-0153, gta Archives, ETH Zürich
[13] F. Otto, Das hängende Dach, Berlin: Im Bauwelt Verlag, 1954, p. 20
[14] Cf. G. Vrachliotis (Ed.), Frei Otto - Denken in Modellen. Leipzig: Spector Books, 2017, pp. 298-303
[15] Cf. H. Isler, ‘Schemaschnitt durch Dachelement’, document unpublished, 23.01.1968, (217-KS-prov-13, gta
Archives, ETH Zürich)
[16] Cf. Behnisch & Partner, ‘Arbeitsbericht’, document unpublished, 19.02.1968, (217-0180, gta Archives, ETH
Zürich)
[17] Olympia-Baugesellschaft MBH, ‘Letter to Heinz Isler’, document unpublished, 08.05.1970, (217-0180, gta
Archives, ETH Zürich)
[18] Cf. H. Isler, ‘Handwritten annotations about the competition proposal’, document unpublished, 06.1967
(217-0180, gta Archives, ETH Zürich)
[19] Cf. H. Isler, ‘New Shapes for Shells’, in Journal of the International Association for Shell and Spatial
Structures (Note 5)
[20] Cf. G. Seifried, D. Sandner, D. Mok, ‘Stuttgart 21, Formentwicklung und Modellierung der neuen
Bahnhofshalle’, in SOFiSTiK-Seminar, Stuttgart, 2004
[21] Cf. H. Isler, ‘Handwritten annotations on the pictures of Frei Otto’s models’, document unpublished,
30.09.1997 (217-02331, gta Archives, ETH Zürich)
[22] Cf. H. Isler, ‘Photo of physical models and annotations’, document unpublished, 07.1998 (217-02331, gta
Archives, ETH Zürich)
[23] H. Isler, ‘Handwritten annotations’, document unpublished, document undated (217-02331, gta Archives,
ETH Zürich)