DS10_01.0: LEARNING wewanttolearn.wordpress.com
marina karamali
a research document on frei otto’s and buckminster fuller’s architecture
university of westminster I london 2011/12 3
4
contents: frei otto: lightweight construction l natural design
7
the birth of form
9
the reverse path
11
the invension of the optimised path systems
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01_tent structures
15
01_experiment
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02_net structures
25
03_pneumatic structures
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03_experiment
35
04_arches l vault l shells
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04_experiment
40
05_branched constructions
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05_experiment
44
06_convertible constructions
49
06_experiment
56
07_umbrellas
71
buckminster fuller: doing more with less
75
synergetics
77
geodesic domes
79
transportation
83
housing
87
alternative map projection
91
experiment_dome
92
experiment_mesh structure
94
documenting the bending possibilities of the structure
96
other geormetries
98
system identification
100
combining the mesh with the tent
102
initial design development
104
form follows nature
107 5
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frei otto: lightweight construction l natural design
(1) spider’s web in detail (2) spider’s web devices
the aim of this research is to investigate the work of frei otto in
order to understand his design principles, which include methods of form developing, study models and as well as an under-
standing of nature. ecological consciousness -to protect not only man, but also life as a whole- is a novelty in the area of
architecture. in this regard, the knowledge of objective evolution of forms in all areas of nature, technology and art plays an important role.
(1)
both for architects and engineers a new way of thinking is re-
quired, especially in the field of ecology oriented towards energy, that is, in the effort to save material and energy, to care for the environment, and to optimise construction.
from
his early work on, otto considered the principle of lightweight construction as a way of building with a minimum con-
suption of material, energetic and economic means. from his perspective, the tents, the cable nets, the pneumatic structures and other types of structures, provided him with a means to reach his objective.
(2) 7
8
the birth of form
(1) (2) (3) (4) (5) (6)
reproductive multiplication cell division actinoptychus diatom radiolaria solenosphera taut spherical pneumatics ramification in non-woody plants wasps’ nest
frei otto’s architecture is closely related to nature in many ways. he has always been designing buildings in harmony with nature. he has been particularly interested on the foundamental aspect of the relationship between architecture and nature. he was an early proponent of ecology, environmental sustainability, and the protection of natural resources. these issues also form the background of his efforts to create spaces using the smallest possible amount of material,
and to produce adaptable, lightweight architecture. “i am interested in the fundamental issues of architecture and construction is the basis of all architecture”.
(1)
as a scientist, frei otto spent his whole life studying the form-finding processes of nature. as an architect he used these processes to develop and build many structures. these are constructions which reveal the processes of their creation with particular clarity. the form-finding processes are those which, given a specified set of conditions and following the prevailing laws of nature,
as they take place without human intervention, they are also termed autonomous formation processes. his work focuses on physical rather than biological autonomous formation processes. this focus does not exclude the processes and forms that are found in living nature. in living nature, too, many give rise to visible forms and constructions under experimental conditions.
form-finding processes are of a physical nature and are not determined exclusively by genetics.
(6)
(5)
(4)
(2)
(3) 9
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the reverse path
(1) specks of fat of various sizes demonstrate surface occupation (2) drawn-out tips of plastic masses (3) shrinkage folds in pollen caused by drying (4) bone structure created by self formation
(2)
(1)
(3)
the
‘reverse path’ method makes it possible to recognise formation processes in animate and inanimate nature to the ex-
tent that such processes are set in motion artificially. this is done by experiment and the technical development of con-
structions. technical developments driven forward at a high level of qualification permit better knowledge of nature’s non-
technical constructions. this is known as the reverse path. it was crearly recognisable that animate nature applies the abiotic self-formation process of bubble formation, and additionally that complex fibre networks of the kind used by technology are necessary and are then found in nature.
(4) 11
12
the invension of the optimised path systems
(1)
(2)
(3)
in terms of model technology it is possible to represent the direct path system in which every traffic starting point is connected by a straight line to every destination with threads. from the traffic point of view, the direct traffic is ideal. but the overall path length and the area used for direct path systems is very large. the minimal path system is ideal for traffic routes and a special experimental arrangement has been devised to investigate it. the model of ‘limited access length’ is suitable for investigating the form of minimal requirement for the manufacture. it can be considered as a compromise between direct path system and minimal path system.
the
minimal path device can reliably determine a minimal path system between any number
of points arranged in any number of ways. the apparatus was developed in 1958 by frei
(1) direct path system, each point connected with all others (2) an 8% over-length is added to each thread (3) branched structure with closed mesh, a minimised detour system is produced after dipping in water (4) minimal path system as soap lamellas between 6 points (5) minimal path system in two generations (6) minimal path system with closed meshs
otto.
(5)
(4)
(6) 13
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01_tent structures
(1)
(1) (2) (3) (4)
four-point tent peak tent arch-supported tent hump-tent soap model
(2)
in the space of only a few years, frei otto developed and built
the most important basic shapes of modern tent construction:
kassel (1955), the peak tents in lausanne, the arch-supported tent in cologne (1957), and the hump tents in berlin. he studied the physical laws of membrane surfaces and exthe simple four -point tent in
plored the fundamental possibilities of the different construction methods.
the
(3)
crucial factors in tent construction are the shape of the
membrane surface and the type of support. the shape of the membrane is the primary factor as it determines its action and the flow of the forces.
in many of his experiments he used soap film to create membrane surfaces in his models. the soap film forms a spatial-
ly curved surface which has specific physical and geometrical properties.
the surface of a soap film is termed a minimal surface as it encloses the smallest possible area within a closed space curve.
(4) 15
(1) plan drawing (2) small pavilion consisting of a double humped membrabe (3) support for the tent
the hump tent is supported by (1)
one or more hump-like high points. the high points can be formed by masts which may have either mushroomshaped heads or heads with flexible lamellae across which the membrane is stretched.
this is a canopy of a cafe in berlin which has star-shaped
wooden leaf springs formed
(2) 16
(3)
the high points. the membrane exhibited an anticlastic curvature everywhere except in the areas above the supporting humps, where its curvature was equidirectional.
(1)
the
peak tent is supported by a mast at a single point within
the membrane surface. the forces of the membrane are gathered along specific lines and then directed to the tip of the mast. this is done by means of valleys reinforced by
cables or straps. it is formed as a space curve with a constant curvature. at the swiss region-
(1)
(1) expo 1964 lausanne (2) general plan drawing of the harbour
al expo 1964 in lausanne, the tent ensemble represented a stylished
alpine landscape.
17
(1) (1) ‘the continuous membrane’ study 1965
18
(1)
(2)
(1) ‘membrane forms’ study model (2) ‘soap film’ model for a tent (3) swiss regional expo 1964 in lausanne at night
(3) 19
01_experiment
the four-point tent has been explored digitally in order to test its performance and reach extreme conditions. a set of variables enables the manip ulation of its geometry.
20
the
four-point structure is here filled with smaller fourpoint particles. 21
an arch-supported tent, physical model
22
through another test of experiments, the four-point tent orien-
tation has been examined against the shades it produces, for a given sunlight direction.
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the
first six orientations. (a-f) show a linear transformation, while at the last three (g-i) the tent’s orientation gave more extreme shading surfaces. (i)
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02_net structures
(1) net roof
(2) abidjan arts centre model (3) the net for the institudde fot lightweight structures was assembled from prefabricated strips.
(1)
cable
nets are essentially subject to the same laws as mem-
brances.
however,
the steel cables allow the construction of
canopies with far greater spans than membrances. all tent types can also be realised using cable nets instead of mem-
unlike membranes, cable nets do not require a specific pattern to form anticlastic surfaces. when a net is stretched branes.
into a saddle shape, its square or rectangular meshes turn to
diamond shapes. if it is possible to change the angles between the cables, a cable net can assume the shape of any surface
(2)
which has a regular curvature. thus it is the edges alone which must be shaped.
the
montreal world expo and the roofs of the olympic buildings in munich consist of preroofs of the
german
pavilion at the
stressed cable nets and belong to the category of peak tents.
to
direct the forces into the up and down points, the typical eyes are used in addition to ridge cables.
a building with many remarkable properties is the aviary which frei otto developed for the hellabrunn zoo in munich. instead
of cables, wires were used to weave a net with a mesh size of 60x60mm.
(3) 25
nets
in a three-dimensional arrangement as an explanation of spatial networks.
model study for a rope cooling tower with minimum surface shape. the minimum surface shape establishes itself in a soap film experiment depending on the diameter and spacing of the rings.
model as part of several form-finding studies for the support of
textile membranes and rope nets, which gave the idea for the pavilion at 26
montreal world fair.
(1) large measurement roof model for the stadium roof.
for the roofing of the main sports facilities in the olympiapark in munich the planners wanted to use tent structures in order
to continue the landscaping in the roofs. the forces in the individual net wires cable were measured mechanically between two net nodes. the model was measured photogrammetrically and with the aid of a three-dimensional measuring bench that recorded the spatial situation of selected areas in co-ordinates.
(1) 27
(1) hellabrunn aviary, the fine-mesh cable net throws a delicate veil over nature (2) the completed bet structure for the exerimental building
the
net for the aviary in the zoo at hellabrunn covers like a delicate, scarcely visible veil a mature meadow landscape woth a large, old trees on the banks of a stream. the character of the net also changes according to the season and the incidence of light.
the (1)
net was made of stainless steel wire and is calculated to
withstand a maximum snow load of 15 kg/m2. it was welded together from strips on the ground, raised on the masts and then arranged in its ultimate shape.
experimental structure was erected on the university campus in stuttgart to test the construction and assembly of the montreal pavilion. it consists of the tensile-loaded steel net
with equal mesh; the compression-loaded steel edge; and 12 guying points, again devided into pressure-and-tensile-loaded (2) 28
components.
the german pavilion at the at the montreal world expo is a re-
sult of years of systematic research on lightweight structures.
“the work stands out for its lively, harmonious and highly differentiated structuring of the exhibition landscape that guarantees a very attractive impression, creating interest on all sides”.
it
was not possible to make linear calculations for the loadbearing structure as a whole, as they were dealing with “an interchange system that was highly statically indeterminate internally, in which deformation would fundamentally influence the force flux”. so they had to restrict their investigations to confining the maximum forces to the individual structural
(1)
members. the advantage of the cable net structure is that all these forces could be investigated in a model and constantly measured and monitored in the built object.
(2)
(1) expo pavilion montreal ‘67, tent skin arch cutting template for the measurement modele (2) regular high-low point area model 29
30
03_pneumatic structures
(1) ballon strung with rope net (2) cushion pneu, dome on circular ground plan, supported at four bearing points (3) convention and exhibition hall, cable-reinforced pneu model
(1)
the
pneumatically stretched membrane represents one of the
most fundamental structural forms in nature.
the
variety of
possible pneumatic constructions is infinite. an endless variety of shapes can be achieved by combining individual shapes, using cables to create waists, adding anchor ropes on the interior of the pneu, varying the pressure conditions, and cutting the membrane to specific patterns. all these variations belong to a specific class of forms which all have an equidirectional surface
(2)
curvature as their defining element. in this way, pneumatic membranes differ in a highly typical fashion from membranes which are tensioned only by an inner prestress and whose shapes are characterised by anticlastic curvature. the shapes of many pneumatically tensioned membranes are reminiscent of biological objects such as body shapes, fruits, or parts of plants.
(3) 31
(1) series of soap bubbles (2) sopa bubbles, foam structure (3) exhibition pavilion at expo 1964 (1)
fair in new york
world
a
soap bubble is a simple example of a pneumatic construc-
tion. it is a thin membrane separating two media which are at different pressures. the stretches acting on the membrane cause it to form a surface which exhibits an essentially equidi-
a perfect sphere results when an enclosing membrane comes under a uniform internal pressure. spherical rectional curvature.
(2)
sectors are formed when a soap film is anchored to a surface. conglomerations of soap films result in foam structures.
the development of technical pneus had its origins in the montgolfier ballons, which were filled with gas of hot air. frei ottos’s words: “from today’s perspective, air-supported halls have a (3) 32
special significance. they represent the most extreme form of lightweight construction.”
(1) free vaulted structures, soaking cloths soaked in plaster solution, suspended and inverted after hardering
shells
can be developed using hanging models with chain
nets. it is possible here to simulate only one aspect in the hanging model -the avoidance of bending forces under a given load, which is usually the dead load.
frei otto
in the 1940s carried out a series of experiments and developed model building methods with the principle of hanging, which can serve to analyse and determine the shape of domed surface struc-
(1)
tures. he tested a variety of different materials and methods, such as models models made of cloths dipped in plaster, fine chains, nets, textile fabrics and many others. 33
34
03_experiment
shells were formed from a hanging model. different patterns of fabric were examined as well as distances of fixed points.
35
36
04_arches l vaults l shells
(1) expo 2000, japanese pavilion, axonometric sketch (2) suspension model for the grid shell (3) grid shell
(1)
a
chain suspended between two points takes on specific form known as the catenary curve. this is a very simple and elementary example of an autonomous formation process in nature. in the given situation, the catenary curve represents an unequivocally ideal shape in which there is only tension and no compression or bending.
unlike
(1)
load-bearing structures in
compression, there is no danger of buckling. thus this system is suitable for very large spans and minimal cross-sections.
frei otto
discovered early in his career that it is possible to transfer an autonomous formation process found in structures
in tension to compressed structures. the tension force in the hanging model becomes a compression force in the inverted structure. the principle of inversion is a human dicovery. inversions of hanging hanging states into standing states, resulting in a zero moment structure, do not occur in nature.
(1) 37
(1) three-dimensional suspension model of the dome with ring compression forces, photographe turned through 180o (2) suspension model
(1)
model for the investigation of load-bearing capacity of the pantheon in rome. frei otto developed two- and three-dimensional
suspension models provided information about the distribution, size and course of the pressure forces. 38
(2)
(1)
(1)(2) reconstructing gaudi’s suspension model (3) chain net suspension models (4) suspension model to find form for groin vaults
reconstructing gaudi’s
sus-
pension model of the ‘colo(2)
nia
guell’
otto
church gave to frei
and his team many new
insights into gaudi’s design methods and about the building of suspension models in general. the work offered a fascinating opportunity for architectural history research.
the
(2)
(3)
model reveals gaudi’s construction methods and provides information about how the church would have looked like if it was built in the basis of the model. 39
04_experiment
(a) plane width: 1
(e) plane width:1 force: -500
(b) plane width: 5
(f) plane width: 30 force: +80
(c) plane width: 10
the deformation of a catenary structure has been digitally analysed. at the diagram on the right, four different width values of the mesh plane have been tested, where a vertical force ap(g) plane width:30 force: +120 moving 40
plies.the range of the force value here, was set from -100 to +100.
on the left, more extreme conditions are shown.
(d) plane width: 20
force: 20
force: 40
force: 60
force: 80
force: 100
+ -
+ -
+ -
+ -
41
42
05_branched constructions
(1) branched constructions (2) suspension model using stiffered threads stiffened with polyester and inverted. preliminary design for an exhibition hall
frei otto developed an early model of branching structures in 1960. in a hanging model, a slab was attached to 64 threads
(1)
which were gathered again and again at different height until they had been collected into four bundles.
the
threads were
stiffened and the model was subsequently inverted.
these
branching structures are usually refered to as tree-col-
but unlike tree benches, bending forces are systematically avoided in the technical tree-like column. the form-finding umns.
process using the hanging model is specifically geared towards eliminating bending stresses. the inner structure of the treelike columns represents a type of framework that is unique in the construction industry.
(2) 43
generation
05_experiment
1
2
1
15o
2
15o
3
4
3
15o
15o
44
rotation angle
4
30o
30o
30o
30o
1
2
3
4
45o
45o
45o
45o
1
2
3
4
60o
60o
60o
60o
1
2
3
4
75o
75o
75o
75o
1
2
3
4
90o
90o
90o
90o
a branch diagram is here examined. the diagram analyses the rotation degree of the angles against the generation level of the branches.
45
plan
and front views diagram of the branch structures.
generation 1
generation 2
angle:15o
angle:15o
angle:45o
generation 4 46
front view
front view
top view
generation 3
visualisation
of a series of
branch structures. although they they are just structural elements, they do provide spatial effects.
47
48
06_convertible constructions
(1) adaptable roof model (2)
the
cannes, erected tent roof
cannes, tent roof being adjusted
(1)
idea of building variably and thus allowing adaptation to
changing weather conditions is indeed very old. even in ancient times mobile roofs were used as a protection against the
sun and to regulate the climate in rooms. convertible roofs are constructed in such a way that their form can be altered as often as it wished and in a relative short time. they solve prob-
lems that can not be trackled by other methods. the diversity of constructions used ranges from simple awnings to relatively
complex mobile domes. frei otto’s development of new light constructions that can be used to span wide areas with the smallest possible outlay in terms of materials and mass, has attracted a great deal of attention to the variability of light constructions. his work produce a new generation of convertible roofs and highly efficient movement systems.
(2) 49
(1)
these
developments make it possible to realise buildings that are there only when they are needed: automatically controlled large-scale tents that can be in place in a few minutes in order to provide protection against the weather.
50
(1) folding membrane roof
(1) ‘multimedia stadium’ 100,000-seat stadium with convertible tent roof sketch (2) (3)(4) opening process
the multimedia stadium was a project carried out in 1970. “our society’s increasing demand for entertaining leisure activities creates a need for large facilities which are flexible enough to adapt to different uses. the mast has a diameter of 5-6m, so that its interior is accessible.
(2)
(3)
(1)
(4) 51
the
membrane roof encloses the theatre with a simple movement. when it is folded it fits behind the spectators.
(1) 52
bad hersefeld open-air theater
(1)
(1)
(2)
(1-4) it takes less than 4 minutes to extend the membrane roof over the theater (5) folded membrane behind the spectators
(3)
(5)
the
open-air productions in the ruined stiftskirche in bad hersfeld required a convertible roof structure that did not affect the historic building and did not impair the spatial impression given by the romanesque setting. the structure consists of a gatherable membrane roof supported by
a central mast. the mast stands by the nave of the ruin, and it is guyed by two cables and 14
guy ropes running like rays over the nave at the front. the guys over the nave are at the same time ferry ropes for the self-driving cable tractors from which the roof skin is suspended.
the roof can be in place within four minutes, and covers an area of 1325 sqm. the form of the (4)
roof was devised using a mobile function model at a scale of 1:50, where the fundamental problems of the gathering and folding of the roof skin were examined and questions relating to the firing process clarified. 53
(1) umbrellas and blinds as possible additive, convertible canopies, 1982
“convertible architecture already has its place among the many architectures of the future, wherever open spaces have to be covered within a few minutes or transformed into completely
closed rooms, the convertible roof will be required. the tent roof has been used for nearly three thousand years and the convertible roofs over the theaters of the romans were the greatest roof constructions of antiquity. for us, convertible roofs are not a historical object but an objective that we have been passionately pursuing for 20 years. we wanted to discover, develop, construct; we wanted to ‘make’ convertible architecture.”
frei otto il5 54
(1)
(1)
“static persistence in unnatural. both dead and living
nature change.
no more here doubts the validity of so-called static architecture. it is our daily handwork, our usual method of building. we are familiar with historically
changeable, adaptable methods of construction, adobe building, the tent, dry brick, the wagon barricade, military and civilian camps, and
we have mobile architecture. then we have convertible architecture, namely the tent roof, tents, shells, lightweight structures.�
(2)
(3)
(1) convertible roofs, study for the sixing procedure (2) umbrella study, 1980 (3) convertible roof, suspended from a high point, 1970 55
06_experiment
folding
/ unfolding procedure of tent fabric along structural axes
perspective view
front view
56
at
the first experiment of a convertible tent design, a set of variables controls the position of points along the basic
structure of the tent. when this variable changes value, allows either a ‘folding’ or ‘unfolding’ of the tent.
57
making
a physical model of the convertible tent. the fabric is
being held along the axes through some links. each of the end links are attached to strings which when pulled make the fabric fold. 58
the folding choreography
59
the tent within a tent
sketch
model of a tent made of four smaller tents. structure is fixed.
60
here
the
sketch
model of a convertiple tent made of four smaller
tents. here the structure is not fixed and the tents open up and fold back, along the cables. 61
62
analysis of a convertible roof structure
1
2
3
4
8
12
16
20
24
divisions
63
a field condition of multiple convertiple structures
condition
divisions: 1st set: 8 2nd set: 8 3rd set: 16 4th set: 12 5th set: 20 6th set: 10 64
a
divisions: 1st set: 12 2nd set: 8 3rd set: 6 4th set: 20 5th set: 10 6th set: 8
condition
b 65
condition divisions: 1st set: 10 2nd set:12 3rd set: 16 4th set: 12 5th set: 8 6th set: 8 66
c
condition
d
divisions: 1st set: 8 2nd set: 6 3rd set: 12 4th set: 12 67
68
the different types of tent fields would then occupy larger areas, as they expand to multiple directions.
condition c condition b
condition d condition a condition d
69
70
07_umbrellas
(1)
pink floyed umbrella, 1978
it can be presumed that the umbrella is the oldest type of convertible roof construction with a small span. it is an archetype, related in form and structure to the yurt and the tepee. umbrellas are known to all cultures as a sign of majesty , symbol of spiritual or secular power.
the
traditional umbrella appeared in various forms, according to material, shape and symbolic content. the simplest form consists of a central rod to which rigid or mobile bars are attached.
in the 1950’s frei otto developed a new umbrella form based on the minimum surface principle. the exclusively tension loaded
membrane of the funnel-shaped umbrella is now stretched un-
der the compression-loaded bars. this construction type made it technically and structurally possible to build very large, convertible umbrellas.
(1) 71
(1) 72
(1) the umbrella while the membrane is being fitted
(1)(2) prototypes of the 5x5 m solar-powered
umbrellas in saudi arabia, 1987 (3-6) prototypes on the coast; opening, when open the umbrellas are 5.4m high, when closed 6.5m.
(3)
(4)
a
convertible shade was to be developed for the great mosque in makkah; it had to be very light so that it did not place too great a load on the
(1)
(5)
structure of the building. the suggestion was made that solar powered square umbrellas should be used. they were developed especially for the pur-
pose. the funnel shape of the individual umbrellas, was derived from soap film studies.
integrated (2)
photovoltaic solar power generation means that they can be opened and closed independently.
(6) 73
74
buckminster fuller: doing more with less
richard buckminster “bucky” fuller was an american engineer, systems theorist, author, designer, inventor, futurist. he had a commitment to “the search for the prin-
ciples governing the universe and help advance the evolution of humanity in accordance with them(...) finding ways of doing more with less to the end that all people everywhere can have more and more”.
fuller developed many ideas, designs and inventions, particularly regarding practical, inexpensive shelter and transportation. it is defined as “applying the principles of sci-
(1)
ence to solving the problems of humanity.”
fuller
believed human societies would soon rely mainly on renewable sources of
energy, such as solar- and wind-derived electricity.
he
hoped for an age of “omni-
successful education and sustenance of all humanity.”
buckminster fuller
was an early environmental activist. he was very aware of the finite resources the planet has to offer, and promoted a principle that he termed “ephemeralisation”, which, in essence—according to futurist and fuller disciple
stew-
art brand—fuller coined to mean “doing more with less” .resources and waste material from cruder products could be recycled into making more valuable products, increasing the efficiency of the entire process.
(1) second world war sketch (2) new deal usa
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76
synergetics
(1)
venetian blind dome
a
system of mensuration employing 60-degree vectorial coordination comprehensive to both physics and chemistry, and to both arithmetic and geometry, in rational whole numbers...
synergetics explains much that has not been previously illuminated... synergetics follows the cosmic logic of the structural
mathematics strategies of nature, which employ the paired sets of the six angular degrees of freedom, frequencies, and vectorially economical actions and their multi-alternative, equi-
economical action options... synergetics discloses the excruciating awkwardness characterising present-day mathematical treatment of the interrelationships of the independent scientific disciplines as originally occasioned by their mutual and separate lacks of awareness of the existence of a comprehensive, rational, coordinating system inherent in nature.
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78
geodesic dome
(1) excersise on ephemeralisation, the ‘monohex’ dome, 1965 (2) fuller studies a geometrical model in his studio
(1)
‘when i inventered and developed my first clear span, allweather geodesic dome, the two largest domes in the world
were both in rome and were each about 50m in diameter, these
st peter’s, built around 1500a.d., and the pantheon, built around 1 a.d. each weights approximately 15,000 tonnes. in are
constrast, my first 50m diameter geodesic all-weather dome installed in hawai weights 15 tonnes. an earthquake would tumble both the roman domes, but it would leave the geodesic unharmed.’
buckminster fuller 1983
fuller
was most famous for his lattice shell structures - geodesic domes, which have been used as parts of military radar stations, civic buildings, environmental protest camps and exhibition attractions. a geodesic dome is a spherical or partialspherical shell structure or lattice shell based on a network of
great circles (geodesics) on the surface of a sphere. the geodesics intersect to form triangular elements that have local triangular rigidity and also distribute the stress across the structure.
when
completed to form a complete sphere, it is a geodesic
sphere. a dome is enclosed, unlike open geodesic structures such as playground climbers.
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(1)
typically
(2)
a geodesic dome design begins with an icosahedron inscribed in a hypothetical sphere, tiling each triangular face with smaller triangles, then projecting the vertices of each tile to the
(1) the automated cotton mill project of 1950 (2) the cornell ‘miniature earth’aphere of 1952 (3) a ‘plydome’ made of sheet material (4) cardboard dome (5) the domes of the us marine corps were the most impressive developed in 1950’s.
sphere. the endpoints of the links of the completed sphere are the projected endpoints on the sphere’s surface. if this is done exactly, each sub-triangle edge is a slightly different length, requiring links of many sizes. to minimise this,
simplifications are made. the result is a compromise of triangles with their vertices lying approximately on the sphere.
(3)
the edges of the triangles form approximate geodesic paths over the surface of the dome.
geodesic designs can be used
to form any curved, enclosed space. unusual configurations may require custom design of each strut, vertex and panel—resulting in a potentially expensive, complex construction; so standard designs tend (4) 80
(5)
to be used.
snelson
and fuller worked in developing what they termed “tensegrity,” an engineering principle of continuous tension and discontinuous compression that allowed domes to deploy a lightweight lattice of interlocking icosahedrons that could be
(1) radomes too led to rapid developments in lightness and fast assembly (2) first production 16.5m radome was built at the bell laboratories (3) the united states pavilion at expo’67 in montreal
skinned with a protective cover. although fuller was not the original inventor, he developed the intrinsic mathematics of the dome, thereby allowing popularisation of the idea — for which
u.s. patent in 1954. the geodesic dome appealed to fuller because it was extremely he received a
strong for its weight, its “omnitriangulated” surface provided an inherently stable structure, and because a sphere encloses the greatest volume for the least surface area.
the dome was introduced to a wider audience as a pavilion for the 1964 world’s fair in new york city designed by thomas howard of synergetics, inc.
(1)
(2)
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82
transportation
‘since i was intent on developing a high-technology dwelling machine that could be air delivered to any remote, beautiful country site where there might be no roadways or landing
fields for airplanes, i decided to try to develop an omni-medium transport vehicle to function in the sky, on the negotiable terrain, or on water - to be securely landable anywhere, like an (1) the wooden framework of the first dymaxion car under construction (2) the interior of the car was finished like a racing yacht
eagle.’
buckminster fuller 1983
(1)
in
the 1930s, fuller designed and built prototypes of what he hoped would be a safer, aerodynamic car, which he called the
dymaxion. fuller worked with professional colleagues for three
years beginning in 1932 on a design idea he had derived from aircraft technologies.
the
three prototype cars were different
from anything being sold at the time. they had three wheels:
two front drive wheels and one rear, steered wheel. the engine was in the rear, and the chassis and body were original designs.
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(1) composite simplified plan and section of the dymaxion car (2) patent application drawings of october 1933 (3)(4)rationalisations for the superiority of the dymaxion’s tricycle wheel arrangement and rear-wheel steering
(2)
(3)
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(4)
(1) isamu noguchi model (2) dymaxion car number three soon after completion (3) the first finished dymaxion car
(1)
despite
its length, and due to its three-wheel design, the dymaxion turned on a small radius and could easily be parked in a tight space. the prototypes were efficient in fuel consumption for their day, traveling about 30 miles per gallon. investors backed out and research ended after one of the prototypes was involved in a high-profile collision that resulted in a fatality.
(2)
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86
housing
(1) the first drawing of the ‘clean-up’ version which has since become world famous, appeared in this form, may 1929 (2) model of dymaxion house first exhibited in
chicago department store in 1929
(1)
the dymaxion house was developed by buckminster Fuller to address several perceived shortcomings with existing home-
building techniques. fuller designed several versions of the house at different times, but they were all factory manufactured kits, assembled on site, intended to be suitable for any site or environment and to use resources efficiently. one important design consideration was ease of shipment and assembly.
buckminster fuller wanted to mass produce a bathroom and a house. his first “dymaxion” design was based on the design of a grain bin. during world war ii, the u.s. Army commissioned fuller to send these housing units to the persian Gulf.
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(4)
(5)
(6)
two dymaxion houses were prototyped – one indoor (the “barwise” house) and one outdoor (the “danbury” house). no dymaxion house built according to fuller’s intentions was ever constructed and lived in. the only two prototypes of the round, aluminum house were bought by investor william fraham, to-
gether with assorted unused prototyping elements as salvage after the venture failed. fuller, a consummate perfectionist, felt he could improve the design and was dissatisfied with the pro-
totype. he refused to begin production rather than allowing the “unfinished” design to be used.
(2)
(1) comparison between the airship-based 4-d towers and conventional housing. (2) later improvements to the originally crude and unstable 4-d towers followed the process of the dymaxion house. (3) convertion of the bathroom into the core of a kitchen and electrical generator for the magazine architectural forum (4) all steel dymaxion unit
(5) ddu involved the design of a new curved segmental lonocoque roof to provide headroom, and the introduction of windows and a convection ventilation system (6) internal view 88
(1)
(3)
(1) wind tunnel tested aerodynamic ventilator rides on cadillac automobile wheel (2) finished house with stainless stell returnable packing cylinder capable of holding all components and fitting into the fuselage of a dc-6 tranport plane
(1)
the final design of the dymaxion house used a central vertical stainless-steel strut on a single foundation. structures similar
to the spokes of a bicycle-wheel hung down from this supporting the roof, while beams radiated out supported the floor.
wedge-shaped fans of sheet metal aluminum formed the roof, ceiling and floor. each structure was assembled at ground level and then winched up the strut. the dymaxion house represented the first conscious effort to build an autonomous building in the 20th century.
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alternative map projection
(1) unfolded photographic dymaxion map with nearly contiguous land masses (2) this icosahedral net shows connected oceans surrounding antarctica (3) a stepping stone on the path to ephemeralization. seeing the world in a new geometry, patened in 1946
(1)
(2)
fuller also designed an alternative projection map, called the dymaxion map. this was designed to show earth’s continents with minimum distortion when projected or printed on a flat
surface. the map is a projection of a world map onto the surface of a polyhedron, which can be unfolded and flattened to two dimensions. the projection depicts the earth’s continents as “one island,” or nearly continuous land masses. The arrangement heavily interrupts the map in order to preserve shapes and sizes.
the dymaxion
projection is intended only for representations
of the entire globe. it is not a gnomonic projection, whereby global data expands from the center point of a tangent facet outward to the edges. instead, each triangle edge of the dymaxion map matches the scale of a partial great circle on a corresponding globe, and other points within each facet shrink toward its middle, rather than enlarging to the peripheries.
fuller intended the map to be unfolded in different ways to emphasise different aspects of the world. peeling the triangular faces of the icosahedron apart in one way results in an icosahedral net that shows an almost contiguous land mass comprising all of earth’s continents – not groups of continents divided by oceans.
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experiment_dome
creating
a dome from paper.
several
layers of the section of
the dome were connected at specific points with every adjacent layer. when unfold, the sections stretch and create those lifghtweight domes. 92
a complete sphere made with the same technique.
93
experiment_mesh structure
making
a mesh structure according to the geodesic dome principles. identical components are connencted and form a simultaneously strong and lightweight structure. 94
assembling the structure.
95
documenting the bending possibilities of the structure_inwards
(1)
(2)
(3)
(4)
(5)
the
connection pattern creates a spiral which enables a lot of stretching on the horizontal direction of the mesh. the vertical axis is much stronger and very little bending is possible.
(6) 96
(7)
(1) normal state (2-5) applying force inwards on the horizontal axis (6-7) applying inwards force on the vertical direction
documenting the bending possibilities of the structure_outwards
(1)
(2)
(3)
(1-3) stretching outwards (4) breaking point
+50% (4)
was the maximum expanding of the structure, before reaching its breaking point. 97
other geometries
a linear orientation was developed and its bending possibilities were tested.
(1)
(2)
(1) the components (2) linear mesh (3-4) circlural bending (5-8) other transformations 98
(3)
(4)
(5)
(6)
(8)
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system identification
(1) 25 individual components were connected (2) recording the deformation (3-6) single row folded back to itself
(1)
testing (2)
100
the bending deformations of the system. was initially examined.
a
single row
(2.1)
(2.2)
(2.3)
(2.4)
(2.5)
(2.6)
(2.7)
(2.8)
(5)
more extreme bending is here applied. the system folds back to itself.
(3)
(4)
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combining the mesh with the tent
(1)
(1) paper pattern (2) folded paper (3-4) spiral skeleton structure (5) frame (6-8) paper set as a skin to the structure
(2)
folded (3) 102
(4)
paper was fitted within the skeleton
the skeleton structure made by identical components was developed to form the support for tents to be set within it.
(5 )
(6)
(7)
(
by inserting more components
as the generations grow, the bending properties of the design allows form deformations to occur.
8
103
initial design development
104
a circular configuration was developed and its deformation was further examined. although its aggressive character, its movement is very smooth.
105
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form follows nature
(3)
the new design will be informed by nature, and it’s performance will be combared with that of the cactus. the principle ideas of collecting and storing water will be translated in an architectural proposal, where the aim will be to survive in the desert.
(2)
(1) cactus (2) reconstruction of trajectorial surfaces in the model of a human femure. (3) schematic representation of the spongous 107