Abstract
Short presentation of the key topics of research of Frei Otto and his teams at IL, with emphasis on the comprehensive investigations on form generating processes, the mutual interdependence of forms as a geometrically measurable, space creating entities and their structural qualities. This was one of the primary research topics at IL, which was studied in different contexties, like prestressed membranes, grid shells, form generation in living nature. Similar questions lead also to the investigations on structures of non-planed settlements, their form generation processes and their characteristics. The article conclude with a short presentation of the author’s latter investigations at the University of Innsbruck, “Institut für Konstruktion und Gestaltung” - “koge” on the phenomena of irregularity and on multilayer membranes, studies which are based on the experiences winned at IL.
Keywords
In remembrance of my more than 20 years of lasting collaboration with Frei Otto at the Institute of Lightweight Structures (IL) (Figures 1 and 2) at the University of Stuttgart, I was asked to prepare a contribution to this special issue of the International Journal of Space Structures, which I do with great pleasure. Indeed, I am really very thankful for all the experiences I could win during the time at IL. There I gained a good base for further studies and teaching activities. In fact, it was an extensive study of the cognition of various kinds of interactions in processes leading to the generation of forms and structures seen as aspects of architecture and nature. At least, I partly will try to share them here.
IL Frei Otto and the author preparing an experiment, photo IL, collection Schaur.
IL colloquium, photo IL, collection Schaur.
The search at IL
Frei Otto was almost constantly engaged in a search for solutions to various questions in different contexts, all aimed for the benefit of men and their environment. From this attitude, his intensive investigations on lightweight structures emerged. Also, later on the extensive inter-disciplinary investigations on the processes of form-generation in living nature were included, as well as other architectural quests. All these studies culminate in the two large interdisciplinary special research projects - ‘Sonderforschungsbereiche’ (SFB) of the German Research Community (DFG): the SFB 64 ‘Wide-spanned Surface Structures’ and SFB 230 ‘Natural Structures’.
The holistic observation of the processes of creating structures, their geometrically quantifiable traits and their structural characteristics together lead towards far-reaching insights in the fields of form-finding, of methodology and of implementing such structures into real buildings with unimagined spatial and technological facets. These also play an important part in the current architecture of free forms, both as an inspiration and as a basis for planning.
Frei Ottos’ careful observations and understanding of the seen enabled him to transform forms generated by tiny soap films (Figure 3) into large buildings with shapes never seen before, with their own inherent beauty coming from their inner equilibrium and unbelievable relative lightness. Tent structures like the ‘Tanzbrunnen Köln’, completed in 1957, now used as a part of an open-air theatre, or the German pavilion for the world exhibition in Montréal, Canada in 1967 (Figure 4), are just two well-known examples. These pioneering buildings rank until today among the most important architectural monuments of the 20th century.
Soap-film model, photo IL, collection Schaur.
German Pavilion for the World Exhibition in Montreal, 1967, stamp.
But also, the so-called grid shells emerge from the equilibrium of all acting forces in its form-finding process with hanging models. These forms, when inverted about an angle of 180 °, generate the funicular surfaces of shells with special structural properties, making it possible to build them very light, and with an amazing simplicity of realisation. A well-known example is the Multihalle Mannheim (Figures 5 and 6); built for the garden exhibition in Mannheim 1975, originally planned to stay for a period of 1 year, but is still standing.
Multihalle Mannheim, hanging Model, photo IL, collection Schaur.
Multihalle Mannheim, photo IL, collection Schaur.
The special characteristic of these structures is constituted by the interdependence of their shapes and their structural qualities. Their forms are the visible result of equilibrium of all acting forces in their form-generating process and because of that they own these special structural qualities. It is this mutual interdependence of the geometrically measurable form and its structural abilities that gives the possibility of lightweight architecture with its fascinating forms and charm of lightness. At the IL, we called such forms ‘selbstbildende Formen’ – self-generating forms. There are different families of them. All forms which belong to one such family follow the same laws, thus constituting their own characteristic form-world. The fascinating thing about such a form-world is its extremely large amount of different highly complex forms, dependent on their edge configurations and eventual interactions in the surface. These two means represent the only instrument to influence these self-generating forms in a creative design process. Frei Otto clearly showed how such design processes can lead to fascinating architecture and to extremely effective structures.
‘Biologie und Bauen’ – biology and building
Being familiar with self-generating forms, well known to us from the countless experiments performed at IL, the recognition of similarities of these forms with some forms of non-living and especially of living nature became apparent.
Similar observations were also made by some other experts, especially the biologist Gerhard Helmcke. An interdisciplinary dialogue started, which finally culminated in a large interdisciplinary investigation on the form-generation in the living nature, the so-called ‘Biologie and Bauen – Biology and Building’ research project (Literature 1). The basic questions were as follows: Are the observed similarities in forms a result of the comparable principles of form generation processes?
and How do the multitudinous forms of the living nature generate? Of cause there is the genetic information, which somehow controls the development of a form, but what kind of physical processes take place, which enables the matter to arrange itself into the respective actual form, like an apple or a particular animal. So the question was in what kind of physical processes self-generation of the forms of the living nature takes place.
Researchers from various disciplines were involved. It was a very intensive search with many inspiring discussions and struggles to gain a clear understanding. The result of these investigations was astonishing. Practically, all forms of the living nature do generate by only one and the same structural principle. This is the structural principle of the self-generating forms of the pneu. Thereby, the ‘pneu’ was defined as: ‘The pneu is a system in which a layer stressed only in tension envelopes a medium’. 1 Pneus are pneumatically strained membrane structures.
The final result of these investigations was summarised as: ‘Pneus are the essential basis for the world of forms of living nature’. 2 This means that the forms of living nature are physically generated by the structural principle of self-generating pneus. Even hard elements, like shells, bones and so on, do often have the typical forms of pneus. Their growth processes are taking place in a soft state within the principle of the pneus and harden later (Literature 2).
These studies provoke the establishment of the SFB 230 (1984–1995) ‘Natürliche Konstruktionen’ – ‘Natural Structures’, a joint interdisciplinary research project of University of Stuttgart and University of Tübingen.
Non-planned settlements
Frei Otto once summarised as one of the goals of this SFB 230 as follows: ‘In this “Special Research Project” we set ourselves the task of studying in more detail the effect of processes of self-organisation, particularly in the area of architecture and of development of towns and settlements’. 3
In the context of the quest of self-organisation processes in development of towns and settlements at the IL, those human settlements with irregular settlement structure (pattern) attracted our attention. Observing them in aerial photographs, we gain the impression that these settlement structures, in spite of their irregularities and diversity of forms, may follow some kind of hidden, more complex order. They somehow remind us of some well-known self-generated forms to us, of our experiments, as well as of some structures observed in non-living nature and even some in living nature. Of course, such analogies can be purely incidental. But we have found again and again that such similarities in the forms of objects of completely disparate areas can originate from comparable conditions of formation.
Such settlements did obviously develop without comprehensive planning. Therefore, we named them non-planned settlements. Their structures seem to emerge from an interaction of many direct self-planning processes and may be influenced by certain self-organising processes. These self-organised processes could lead, regardless of their cultural and historical background, to certain possibly common characteristics of non-planned settlements.
These assumptions needed to be investigated; methods for such investigations had to be developed. Frei Otto entrusted this task to me as my PhD work (Literature 3). The investigations were carried out as a part project of the SFB 230.
How to start with such a study? The sources of information were, as already mentioned, aerial photographs, in which the settlement structures were well recognisable (Figures 7 and 8).
Sokota, Ethiopia, photo Georg Gerster, Zumikon, Zürich, collection Schaur.
Harar, Ethiopia, photo Georg Gerster, Zumikon, Zürich, collection Schaur.
Method of investigation
The large diversity of forms of this kind of settlement structures required special methods of investigation, which first I had to develop. In order to find out whether such settlement structures do have common characteristics and whether they could result from processes comparable with the self-generating form-formation processes of self-generated forms, those structural characteristics had to be identified, which despite the complexity of the observed structural forms can be objectively comprehended, measured and compared.
There are two aspects which play an important role in any process of the formation of a settlement without an overall planning. One is the occupation of the land by individuals, and the other is the path system which makes all these sub-areas accessible. In this way, the path system divides the settlement area in numerous sub-areas. These two aspects, the sub-areas and the path system, form the settlement structure, which is well visible and which was observed (Figures 9 and 10).
Sokota, settlement structure, drawing Eda Schaur.
Harar, settlement structure, drawing Eda Schaur.
Such a settlement structure can be seen as a network. This has two kinds of characteristics: (1) metrical, which includes the precise form of all paths and the sub-areas, and (2) topological, which is clearly ascertainable in spite of the complex forms. So, the topological characteristics of settlement structures represented an important feature for the investigation.
The topological features of the structures are manifested by two characteristics. One is the kind of nodes, which is expressed in the number of lines – paths, which form a node (Figure 11). The other represents the neighbourhood relationships of the meshes – the sub-areas, which exist between sub-areas separated by paths. Here, the number of the neighbours of each sub-area was identified (Figure 12).
Nodes, sketch Eda Schaur.
Neighbourhood relationships, sketch Eda Schaur.
Structures with identical topology can take very different forms, which can be illustrated by a net drawn on a rubber membrane. Each time the membrane is stretched, the form of the net changes, but not its topological characteristics.
In addition to the settlement structures, in the investigation, self-generating structures were also included, which may be related to the settlement structures. These were two systems of interconnection, which could play a role in the formation of the path system, the minimal path system and the minimal detour system. Then two others were included, which represent methods of occupation of a surface and its division into sub-areas, the bubble float (Figure 13) and structures created by flowing sand models (Figure 14).
Bubble float, photo IL, collection Schaur.
Flowing sand model of Sokota settlement structure, Eda Schaur.
Furthermore, some structures of non-living nature, like crack patterns (Figure 15) and some of living nature, like the supply systems of leaves (Figure 16) and of the dragonfly wing, as well as the geometrically-formed nets, such as the direct path system and the regular grids, the triangular, the square and the hexagonal grid were also included in the comparative studies.
Crack pattern, photo Kage Manfred, Institut für wissenschaftliche Photografie, in Hildebrandt S and Tromba A. Panotptimum. Heidelberg, 1987, p. 11.
Maple leaf, photo Klaus Bach IL, collection Schaur.
In the range of metrical features of the structures, the detours of the path systems were investigated. The detours give information about the efficiency of a path system. If a path between points A and B deviates from the shortest imaginable connection of a straight line, it is longer and represents a detour, which is expressed as a percentage. These studies required comprehensive calculations and were done within the SFB 230 in cooperation with the ‘Institut für Anwendung der Geodäsie im Bauwesen (IAGB)’ of the University of Stuttgart. In a stimulating cooperation with Matthias Neureiter, we developed a new tool, which allowed us to display various detour characteristics of the path systems for the first time.
Results
To get answers to the initial questions, a comparative study of the found features of all the individual examples was done.
In the path systems of non-planned settlements, a clear predominance of three-armed nodes was discovered (73–100%). This means that most of the nodes of these systems are formed either by branching of a path into two ‘branches’ or by a path leading into another. Four-armed nodes were considerably less frequent. Even the relatively rare four-armed nodes only rarely had the form of a crossing, the form well known to us from planned settlements. Nodes with five or more arms were seldom found and if so, they mostly form a ‘square’.
In most of the investigated self-generating structures, the bubble float and structures created by flowing sand, crack patterns in the surfaces and the supply systems of leaves and of the dragonfly wing, the predominance of three-armed nodes is even more strongly pronounced as in the settlement structures (83–100%).
The minimal path system and the minimal detour system constitute exceptions. The minimal path system possesses only three-armed nodes, but it is an open-branched system, which forms no sub-areas. In the minimal detour system, four-armed nodes (48%) predominate, followed by three-armed nodes (34%), which is not astonishing as this system originates from the direct path system in which nodes are formed by crossings of independent connections.
In the other topological characteristic of the structures, the neighbourhood relationship of the sub-areas, the diversity was characteristic. The sub-areas of non-planned settlement structures have quite different numbers of neighbours, between two and sixteen. In each of the settlements, at least eight different neighbourhood numbers were found. This lack of uniformity of neighbourhood numbers is expressed in a relative small proportion of sub-areas having identical number of neighbours. Nevertheless, four or five neighbours prevail, but these maxima are very low between 24% and 36%.
The studied self-generating structures mainly agree with these features. The dragonfly wing in which six neighbours prevail (63%) is the exception.
These two topological characteristics of the investigated examples clearly showed topological similarities of the structures of non-planned settlements. They actually form a single structural family. This is widely in common with the self-generating forms generated by occupying an area. The diagram in which each structure is characterised by the average node type number on the horizontal axis and the average neighbourhood number on the vertical axis illustrates this feature. Herein, each settlement is represented by a dot, and each self-generating structure is represented by a cross (Figure 17). The hexagonal grid has more resemblance to these structures than the square grid, which possesses very different features and is closely related to the structures of the planned cities.
Diagram of topological features of examined structures, IL 39, Non-planned Settlements, p. 192, drawing Eda Schaur.
Settlements
A1 – African village 1;A2 – African village 2; A3 – African village 3; AM – Ahmedabad old city, India; DA – Village in Ethiopia; BI – Bida, Nigeria; HA – Harar, Ethiopia; IS – Istanbul, Turkey in 1846; KA – Karagedik, Turkey; L55 – Labbezanga, Ethiopia 1955; L73 – Labbezanga, Ethiopia 1973; DM – village in Mali/Martina Franka, Italia; NA – NB village between Nartron lake and Serengeti, Tanzania; SU – Shushtar, Iran; SO – Sokota, Ethiopia; TB – Tell Bisse, Syria; TI – Timgad, Algeria; and YA – Yaguine, Mali.
Self-generating structures
AB – maple leaf; BL 1 – bubble float 1; BL 2 – bubble float 2; BL 3 – bubble float 3; DW – 12 point direct path system; FM – 12 point minimal detour system; GR – crack pattern in gelatine; LI – dragonfly wing pattern; PR – China glaze crack pattern; and SM – flowing sand model of Sokota.
Within these topological characteristics found in my studies, a multitude of forms of the settlement structure can develop.
The investigation on the detours of the path systems could only be done for a few examples. Thereby, the lowest average detour of the whole network system was achieved by the bubble float (22%), followed by the path systems of the non-planned settlements (24–24.5%). The hexagonal grid has an average detour of 27% and the square grid is slightly higher with 27.35%.
The outcome
The comparative studies of the topological characteristics of a non-planned settlement clearly revealed the structural affinity of such settlements. These obviously constitute a single structural family, which they share with the studied self-generating structures of surface occupation. The free choice of the occupation of land by individual groups seems to have a decisive influence on the structural formation of non-planned settlements. Simultaneously, the relatively low detours show an attempt towards an efficient path system.
Eventually other universal factors of structural formation, possibly based on universal human patterns of behaviour or social or other factors, were not taken into consideration. These may constitute topics for further investigations.
Within the topological structural characteristics found, there remains a considerable freedom for the development of the most varied forms of individual elements, as well as for the entire settlement structure. Most likely, the adaptation of a settlement to the geographical and topographical, possibly even cultural, peculiarities largely takes place within the metric properties of the settlement structure (Literature 3).
‘KOGE’ – Institut für Konstruktion und Gestaltung, Universität Innsbruck
Based on the experiences of the investigations at IL, we continued the studies on different aspects of forms, their form-generating processes and their structural qualities at the ‘Institut für Konstruktion und Gestaltung’ Institute of Structure and Design “KOGE”at the University of Innsbruck. This institute was fully involved in the teachings within the faculty of Architecture and at the beginning as well on the Faculty of Structural Engineering. So, the investigations were integrated into teachings in a way that the students examine different sectors of the experimental topics. Using these, a broader understanding grows over the years. In the following, two topics of these studies are shown.
The phenomena of irregularity
As it was seen on the structures of non-planned settlements, the irregularity allows a huge range of variations of actual forms, according to the individual needs of their inhabitants. So, the phenomenon of the irregularity may also be of interest in other contexts.
In Innsbruck, I started to investigate structures with irregularities. In these studies, we concentrated on systems in which the whole structure was created by irregular arrangement of the elements. If one assumes that a certain kind of irregularity of structures may represent an interesting freedom in a design process, then the following questions arise:
How large is such a freedom and where are its limits?
What does the irregularity mean for the creation of architectural spaces?
Would such irregularity of structures fascinate us like the irregularities of objects in nature often does?
How do such irregularities influence the stability of structures? This is a reasonable question, as the form by itself represents an important structural quality, as seen above. In nature, the form as we perceive it with our visual perception and as the structure, which gives the required stability to the object, are always united, are one and the same. In the human analytical approach, these two aspects of forms and their mutual influence are to seldom considered.
We started these studies with a very simple but convincing approach, an experiment in which an arch should be created out of straight, flexible elements. The predetermined form of the arch – a catenary – should be achieved only by the irregular arrangement of the elements. The joints of the elements were not fixed but allowed rotation. After assembling the elements, the arch took almost perfectly the predetermined form and gained its form and structural stability (Figures 18 and 19).
Arch – irregular structure, ‘Methoden des Leichtbaus’, 2006 – Schaur, Institut für Konstruktion und Gestaltung (KOGE), photo Jens Meier, collection Schaur.
Arch detail – irregular structure, ‘Methoden des Leichtbaus’, 2006 – Schaur, Institut für Konstruktion und Gestaltung (KOGE), photo Jens Meier, collection Schaur.
The same was observed with shells constructed by irregular grids (Figures 20 and 21). Classical grid shells constructed by primary square grids require additional elements to get their form stability. Shells with the irregular grids do not require such additions. The irregularity of the grid simultaneously represents an interesting potential for the design process, as it offers the possibility of uniting the requirements of design with that of the structure.
Grid shell side view – irregular structure, ‘Übung Konstruktion + Gestaltung’ 2011 – Schaur, Students: Fillinger/Kurz; collection Schaur.
Grid shell topview – irregular structure, ‘Übung Konstruktion + Gestaltung’ 2011 – Schaur, Students: Fillinger/Kurz; collection Schaur.
The composition of stiff surfaces, plain or curved, and its connection by columns, is another fascinating example. The connection between the columns and the surfaces is that of hinges. There has to be a group of at least six columns to keep these two surfaces at a constant stable distance. But when these columns are placed parallel to each other, the structure will collapse in itself. As soon as the columns are inclined in different directions, they form an irregular arrangement and the structure is stable (Figures 22 and 23).
Six-column model, Schaur/Oberwalsder, KOGE 2005, photo Jens Meier, collection Schaur.
Six-column model connected with a grid shell, seminar ‘Processes of Form-finding’ 2010 – Dickson/Schaur, Students: Lieb/Oberdorfer, collection Schaur.
Thereby, the arrangement of the columns offers many possible variations. They can be spread free over the surface or be arranged just in the edge areas or in the middle area of the surfaces. Such a system can be even vertically stacked (Figure 24).
Vertical addition of the structures with irregular columns arrangement, ‘Processes of form-finding’, 2006 – Schaur, KOGE, photo Jens Meier, collection Schaur.
These few examples indicate the potentiality of the phenomena of irregularity as a freedom for a design and simultaneously as a remarkable structural property of a system. They show very clearly the mutual interdependence of the two aspects of forms: the visually perceived aspect and the structural aspect. They most properly also represent an answer to the question: How large is the freedom of irregularity, and where are its limits? This may represent an interesting field for further investigations (Literature 4).
Multilayer membranes
Another experimental topic at the “KOGE” belongs to the field of prestressed tensile structures, the well-known tent structure, like the roofs for the Olympic Games in Munich 1972. These are the so-called multilayer membranes. They differ from the known prestressed tent structures by the fact that here several layers of membranes are brought in interaction and melt thereby into a new whole.
Multilayer membranes consist of at least two or more layers of prestressed membranes, which are interacting. They mutually form / configure each other and thereby create a spatial system, which generates spaces below it and inbetween the layers.
Continuous spatially curved surfaces run fluently through the space, approach each other, touch, go over into each other and run apart again. Multilayer landscapes that were never seen before originate in this way (Figures 25 and 26).
Model study with an overturning membrane, ‘Design Studio’ – Schaur/Hallama, photo Jens Meier, collection Schaur.
Public space NY, ‘Design studio 2’ 2011 – Schaur/Hallama, students: Reitzner/Stern, photo Jens Meier, collection Schaur.
The aim of our investigations was to discover these fascinating entities, to study their laws of form formation and to reveal their form-world.
Although they belong to the family of the prestressed membrane structures, they constitute an own form-world with multitudinous individual forms, all following the same laws. Also the forms of the multilayer membranes are self-generating phenomena, which generate/arise as the result of the equilibrium of all active forces. Therefore, their forms cannot be arbitrarily shaped, but they can be influenced by different kinds and arrangements of their edges and various ways of the interactions of the individual membrane layers. By these means, multitudinous different variations can be generated.
We behold them as architectural entities and try to adumbrate their possible meaning for architecture by studying them in various architectural contexts (Figures 27–29).
Public space over the River Inn, ‘Design studio’ 2012 – Schaur/Hallama, students: Leitgelb-Spörk/Ivan, photo Jens Meier, collection Schaur.
Open Air Performance Area over a Canyon, ‘Design studio 3’ 2012 – Schaur/Hallama, students: Wagenhofer/Westreicher, collection Schaur.
Public space NY, ‘Design studio 2’ – Schaur/Hallama, model KOGE 2011, students: Reitzner/Stern, collection Schaur.
Conclusion
The interrelation of the two aspects of forms, on one side their architectural potentiality of space creation and simultaneously their inherent structural potentiality which can lead to very logical and effective structural solutions, represents a very large field of search. Frei Otto and his teams with their comprehensive work, their extensive research and their pioneer buildings showed in a very clear and extremely impressive way what the results of such an approach can be. Thanks to this work, our eyes and our minds get opened. There may be brave people or interdisciplinary groups of researchers with intensive interest and perseverance, which may still further broaden the insight into this fascinating field.
Footnotes
Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.
Funding
The author(s) received no financial support for the research, authorship and/or publication of this article.
Further reading
Literature 1.
Frei Otto, Berthold Burkhardt and others: IL3 ‘Biologie und Bauen 1 – Biology and Building 1’, Stuttgart 1971.
Frei Otto, Berthold Burkhardt and others: IL4, Stuttgart 1972.
Frei Otto, Klaus Bach and others: IL6, Stuttgart 1973.
Literature 2.
Frei Otto, Eda Schaur and others: IL9 ‘Pneus in Natur und Technik/Pneus in Nature and Technics’, Stuttgart 1977.
Frei Otto, Cornelius Thywissen and others: IL19 ‘Wachsende und sich teilende Pneus/Growing and Dividing Pneus’, Stuttgart 1979.
Frei Otto and others: ‘Natürliche Konstruktionen’, Stuttgart 1982.
Literature 3.
Eda Schaur: IL 39 ‘Ungeplante Siedlungen/Non-Planned Settlements’, Stuttgart 1991 (submitted as PhD thesis in September 1990).
Literature 4.
Eda Schaur (HG) Konstruktion und Gestaltung – Neue Formwelten für Architektur, Innsbruck 2013, Eda Schaur, ‘Das Phänomen der Irregularität’, pp. 129–145.
Literature 5.
Eda Schaur (HG) Konstruktion und Gestaltung – Neue Formwelten für Architektur, Innsbruck 2013, Eda Schaur: ‘Multilayer-Membranen’, pp. 16–91.