BUCKMINSTER FULLER
WORK:
INTEREST:
METHODS
A CRITICAL LOOK AT FULLER’S SCIENCE
FULLER’S VIEW OF THE WORLD
Born in 1895
More with less -less material -less waste -answer to traditional building
Efficiency in all parts of life, not only architecture
Fanatical (24 hour workdays full of testing, modeling, measuring...)
Nature influenced: (strongest viruses have geodesic forms, crystals, chemistry in general)
Self sufficiency (including central ventilation system, fuel tanks, energy sources including alternative energy sources, water supply)
Traveling: he was one of the few who looked at the issue from a global perspective.
No objects: in his opinion thinking about buildings in terms of objects will never solve the energy crisis. We should assume that all things are connected in systems.
Rebellious child (despised those who made fun of people who wanted to be original) Expelled from Harvard twice Trivia: to be noticed, Buckminster Fuller would walk around with a wolfhound Joined navy: -learned to be comprehensive -learned him about efficiency / self sufficiency which later informed his architecture In 1927 after the collapse of Stockade personal problems began: -suicide attempts -creative breakdown -drawing with self destructive energy 1930 predictions about human numbers influenced his future work The character of Buckminster Fuller is hard to explain: highly motivated ego, infectious optimism, in many situations naive.
Stockade system -same strenght / less material -brick walls become structural after concrete is poured into holes in them Fuller Houses were his more succesful attempt to run a bussines. Prefabrication and mass production of houses built out of as little material as possible. 4D houses: He believed we should not build houses only in 3D but also consider time as a factor in terms of use of materials, climate, shape etc. Shapes that last longer were by his opinion the circular shapes, hence the geodesic dome. Dymaxion car: -light -aerodynamic -energy efficient -silent Dymaxion house: -extremely energy efficient -unfortunately the time was not right (no interest in environmental issues, because there was no profit from them.)
Project One: Learn Buckminster Fuller by Luka Kreze
Climate: Buckminster Fuller is the pioneer of environmental design and forward thinking in terms of the climate, as a response to the predicted growing people numbers Energy use: energy should not worry us until the sun shines. He was one of the first harsh critics of use of gas. In his words if we cannot find alternative sources just yet, we should at least use the technology we have to use those in a more efficient way.
Models: he saw them very practical and was critical that other architects do not use models as much as they used to. In his words designing with the aid of models was the only way to design (if you don’t touch it is not true) Testing ( systems, sample materials etc.) lead to innovations and patents. Writing: his recording was very thorough, very analytical but sometimes incoherent.
Science over art
Patenting
Durability (little maintenance was required in all of his houses)
Selling: eventhough he was many times wrong in his calculations, he was amazingly good at publicity and presentation of his work. He was good at bending statistics, charm with secrecy and was very successful in using his ego for promotional purposes.
Progress by creation, not destruction: better materials, better procedures mean better houses.
On the outside his technology seems very scientific, however he would ignore some data that did not suit him Focusing on technology too much would sometimes cause that he would forget about topics such as sociology, demography etc. Fact vs. fantasy? eventhough many of his ideas were believable, his naive belief in almost science fiction like ideas would harm the credibility of his ideas about topics such as energy efficiency. In his entire career he never forced people in a certain way of living as a result of technology (whereas some of his colleagues would argue that a person has to adapt to technological process and live by the rules technology sets.)
Systems (e.g. sphere, a perfect system where all points are equally distanced from the core. Units (parts of a system, instead of objects). Examples would include a group unit, family unit or basic unit. Cycles: he would consider all the aspects of a building e.g. characteristics of the Witchita house: 1. Mass production 2. Package distribution 3. Quick erection 4. Low cost 5. Flexible orientation 6. Resistance (fire, earth quake) 7. Air protection 8. Demountability Vector equilibrium (in a perfect system all the forces/energy cancel) Decades before any of such concepts were even mentioned, Buckminster Fuller was thinking about dwellings as ecosystems.
FREI OTTO
IDEAS
INFLUENCES
NATURE
Born in 1925
Architecture is not a matter of self presentation or made to influence only one client but is made to make the entire society a better place to live.
Admission into Air force
Frei Ottos response to cult of personality architecture was natural architecture that had it’s roots in self organization and economy principle of nature.
Studied in Berlin Went into air force (the same way Buckminster Fuller went into navy) The air force inspired him with the lack of resources (again in the same way as Buckminster Fuller). The air force experience hence influenced his future work. Studied in the USA (Mies van der Rohe, F. L. Wright, Buckminster Fuller) First building was the music pavilion in Kassel (already a tensile structure) Best known works : -Munich Olympic Stadium and park -Melbourne music bowl Founded the Institute for Lightweight Structures in Stuttgart One of his latest works is the pavilion for 2000 EXPO, together with Shigeru Ban.
Humane architecture: peaceful human coexistence (earth is for mankind). Might be one of the reasons why he was so interested in tents, since they have a strong historical connection to coexistence. Peace and harmony with nature Light and mobile architecture (lightness against brutality). He was one of the rare architects (together with Buckminster Fuller) who had a clear idea about his work that was not based purely on any ideological, personal, technological agenda but also focused also on the social part of the issue. Adaptability: buildings have to be able to adapt (expand/shrink if necessary) Gestalt werdung: emergence of form in nature and technology Ecology: -environmental sustainability -resource protection
End of war (he saw the architecture of war as the architecture of killing) His agenda was to help rebuild after war. Burning cities: “Hard introductory course for every young architect.” Rejection of Nazi architecture: most of this kind of architecture tried to impress with mass and to present its durability not trough quality materials but heaviness (eternity). In a answer to that Frei Otto’s architecture was the architecture of lightness, rejection of prestige and no symbols. Trend at that time was dematerialization of architecture (materials such as steel, glass, fabric etc.) and disappearance of the historical form (also in Bauhaus)
He regarded natural objects as structures. Natural processes fueled Frei Otto’s natural construction. In his opinion humans should exploit the natural processes for their own purposes (technology) which would help us especially with reducing materials to a minimum. Frei Otto’s structures influenced by nature include: 1. Tents: 4 point tent, peak tent, arch supported tent, hump tent. (Extremely important are Frei Otto’s experiments with soap films which helped him to research the stable membrane surfaces. 2. Pneus and hydros: thin membrane separates two media at different pressures. These shapes offer designers infinite possibilities. 3. Suspended constructions 4. Grid shells
by Luka Kreze
LITERATURE
Huch Kenner: Bucky - A Guided Tour of Buckminster Fuller Frei Otto: Schriften und Reden 1951 . 1983
His architecture was in harmony rather than in opposition with nature.
5. Branching structures Project One: Learn Frei Otto
PICTURES
Fig. 1 above: Buckiminster Fuller - Witchita house Fig. 2 below: Buckminster Fuller - American Pavilion (in flames 1976)
Peter Gosney: Buckminster Fuller and the Energy Crisis (Diploma in Architecture 1996) Lorreta Lorance: Becoming Bucky Fuller Frei Otto: Complete Works - Lightweight Construction Natural Design
Fig. 3 Below: Frei Otto - Munich Olympic Park
BRANCHING STRUCTURES
NATURE AND EVERYDAY LIFE
IL STUDIES OF SHAPES AND MINIMAL PATH (EFFICIENCY)
FORCES AND THE SHAPE - COMPRESSION, TENSION
Branching structures are based on geometric systems that expand through bifurcation without returning to form closed cells. In this sense, branching structures resemble the structure of trees that branch continually outward. In architectural engineering, these forms can be used either as tension or compression systems.
Natural systems and branching structures, among others, share many notions about efficiency. Eventhough there are some differences in how e.g. trees and tree-like structures from real life construction spread their loads, they are all rational in terms of minimal path (as little detour as possible) and material use. Examples below include trees, rivers and electrical distribution grid.
Frei Otto: Minimal path system (below)
In determining the ideal shape of systems loaded in compression, the level of the load plays a role in the optimal geometry. With higher load levels the most efficient member lengths are longer. For the lowest level (far left) the nodes shift to find the geometry with minimal member length (minimal path) since the force is of secondary importance. A progressive lengthening of the upper ‘branches’ can be noticed as the load increases. In the second scenario the upper two nodes are constrained. The effect of lengthening of members now can be seen below the constrained nodes.
One of the branching structures’ benefits is that they are extremely effective when the constructional task is to transfer loads which act separately on a larger area and must be transferred across a specific distance to individual points of support (e.g. ceiling or roof loads which are transferred to individual foundations). System of the branching structure is based on a principle Frei Otto calls minimal path system, meaning that the distance between the individual nodes (length of the structure members) is the smallest possible. Because of this two principles branching structure is very efficient in terms of material use since it requires much less material as e.g. vertical columns. The shape and direction of the structure (or its members) is similar or the same to the forces that travel from the load to the final fixing point.
Project One: Learn Branching Structures by Luka Kreze
By creating soap films (always create minimal surfaces) between adjustable needles, water and glass he created a pattern that touches all the needles and has the shortest possible length.
Marek Kolodziejczyk (bottom left) used string models dipped in water to find a pseudo minimal path forms produced by the water surface tension on the strings Jürgen Hennicke (bottom right) used dry string where beads allow positioning and repositioning of the nodes and the length of threads can also be adjusted in the frame.
The figures on the right hand side are showing forms derived from a tensile loading. The same 4 load levels were chosen. In the case of tension, the lower vertical stem disappears except for the very low load level.
PNEUMATIC MEMBRANES WITH INTERNAL DRAINAGE Pneumatic structures are tensile stressed structures that use air to carry the load. Eventhough they are because of this notion in a way related to suspended structures it is hard to place pneumatic membranes among either column/beam, archsupported or suspended structures. The internal forces on the membrane act normal to the surface of the membrane, hence the structure is free of stress under a positive load.
The easiest way to explain how the structure works is by an example: if we assume the membrane weights 1kg/m2 the pressure of only 1kPa/ m2 will be needed to hold the structure in place (example above). In case of uniform load (e.g. snow) of 75kg/ m2 the required pressure is 76kPa/ m2. (below)
BENEFITS
ADAPTABILITY
LOADING EXPERIMENTS
AESTHETICS
EFFECT OF PNEUMATIC MEMBRANE STRUCTURE ON MAN
Pneumatic membranes with internal drainage (PMIDs) are especially beneficial in cases where large areas need to be covered with a relatively low structure. Shallow arches are subject to high tension caused by a large radius of curvature. PMIDs have internal points of anchoring and so they require drainage. Because of those anchorings the spans of curvature are minimized and hence the membrane tensions are smaller. The forces in membranes depend on distances between drainage points. Buckling in these structures does not exist hence the spans can be extremely long, from 100m to (theoretically) up to several kilometers. In this view pneumatic structures are highly economical (material vs. area ratio.
The structure of the pneumatic membranes with internal drainage can be extended at will at uniform average height. PMIDs are one of the most economical large area roofings and are independent of the configuration of the enclosed terrain, they can be anchored in almost any soil, under water, they can be joined to form larger parts even more economically etc.
Several experimental models have been developed to test the performance of the pneumatic membranes. The experiment below shows the measuring of the indentation depth (load 150mm on 100m2 disks). The internal pressure was remained constant and indentations did not cause any bulging
Pneumatic structures can achieve incredible visual effect especially when structural aesthetics meets the correct materiality. Some of the following examples such as Chicago Convention Hall bellow represent perfect example where grandiosity fights delicacy and peace
Eventhough some might say living “under pressure� is unhealthy, in reality the maximum internal pressure corresponds to an altitude change of only 55m whereas normal pressure corresponds to about 15 of altitude change. Is life under a pneumatic membrane really only utopia?
LITERATURE Above: Pneumatic membranes can be extended, elevated, transformed simply by adjusting the height of internal or external anchor points, or made flatter by using external ropes to maintain the tensions. Below: Examples of drainage systems (below) show two of many ways to deal with drained water without affecting the internal pressure.
Frei Otto: Schriften und Reden 1951 . 1983
Fig. 3 Below: Frei Otto - Munich Olympic Park
Frei Otto: Tensile Structures Frei Otto: Complete Works - Lightweight Construction Natural Design Peter von Buelow: A Geometric Comparison of Branching Structures in Compression and Tension Versus Minimal Paths Frei Otto, Bodo Rasch: Finding Form. Towards an Architecture of the Minimal
Project One: Learn Pneumatic Structures WIth Internal Drainage by Luka Kreze
EXPLORING MATERIALS
COTTON (FAILED)
RUBBER
TIGHTS (FAILED) My first experiment that was supposed to test how the pneumatic structures work when the internal anchor is added was conducted by using lady tights, a canvas and 2 kilograms of rice to mimic the air particles. I wrapped the canvas base in tights, filled up the space between them with rice and then anchored it in the center point. Since tights are knit as a loose “gridshell” where vertical strings have almost no connection to the horizontal ones (they slide on top of each other) the tights ripped very quickly.
In the second experiment i tried to find a material that is a bit stronger so I repeated the same procedure with cotton. Cotton can withstand pressure so there were no problems with ripping. Other flaws presented, however, Since I was dealing with a relatively small surface, cotton proved to be too rigid, thick and inelastic because of the thickness of strings and the way they are intertwined.
In my next attempt I decided to use a material that is thin, flexible but still relatively strong. Instead of a material to mimic the air particles I decided to actually inflate the rubber condoms and then find a way to add the internal anchor.
Cotton experiment did answer some questions about elasticity. Since the material is rigid the maximum shape (moment when no more rice can be added) is very quickly achieved. I have also learned about the relationship between material elasticity and curvature. In the case of cotton, the curvature is very low. The slope between the anchor point and the top of the “hill” is very subtle. (see the bottom left curve). The curvature of the right side curve belov is what I am aiming for.
Picture above is a close-up of the tights material structure.
Project One: Learn Exploring Materials by Luka Kreze
Picture above is a close-up of the cotton material structure.
I inflated the tip of the condom, anchored it trough a hole in the base (a cap) and inflated the condom above the cap to get a wanted shape.
My aim was to create a stronger internal anchor for the membrane.
I had to find a way to tie the base and the tip of the condom together (to avoid the air leak) and to keep the base only for stability and shape.
RUBBER EXPERIMENTS
RUBBER + STRING In my third attempt of using condoms as the membrane I decided to tie the tip of the condom to a string, turn the condom inside out, pull the string trough the hole in the base and inflate the entire apparatus (above). When the string is pulled it acts as an internal anchor, the more we pull, the steeper the curve and the more is the membrane in tension. The two pictures on the right hand side show the same procedure without the use of the base.
Project One: Learn Rubber Experiments by Luka Kreze
SELF ANCHORING
INSPIRATION FOR FUTURE PHYSICAL MODELING
In the final shape that I tied one anchor of the membrane (the tip) to the opposite side of the balloon. The forces in the balloon balanced in a way that resulted in an almost torus shaped “two anchored” structure with two same length anchors. This is only true if no external forces are applied to one of the sides. If we put pressure to the left or the right side of the anchors, the anchors will extend in length and shift to the area with lower air pressure. If we put pressure on the anchors, they will get shorter, the slope to the anchors will decrease, the structure will flatten and expand away from the anchors.
P - WALL by Matsys The wall explores the self-organization of material under force. Using nylon fabric and wooden dowels as form-work, the weight of the liquid plaster slurry causes the fabric to sag, expand, and wrinkle. It has its origins in the experiments of earlier, 20th century architects including Antoní Gaudí and Miguel Fisác, both of whom investigated the potential of cast material to yield unique, sensual and, at times, bizarre shapes
TREE MODEL
PHYSICAL MODEL
GRASSHOPPER MODEL In my next attempt of using Grasshopper to model a tree structure I created a SDL line and assigned its direction by using XYZ vector. Z-value is always set to 100 while Y and Z change for every of four branches. In every story number of branches is 4 times bigger than story below. Top point of every branch is a starting point for four SDL lines of branches in the next floor. Fig. 1 (above): Grasshopper definition is for now much too complicated.
RUBBER + STRING
Fig. 2: Definition for a single branch (above) and digital model for 3 level branching structure (below)
Project One: Learn Tree Model by Luka Kreze
LEARNING FROM P-WALL
FORM FINDING / RICE
The model is created in a following way. A timber frame holds an elastic membrane in place above the wooden dowels which are inserted into holes in the base. The holes are arranged in a grid so that dowels can be rearranged if needed. When plaster is then poured onto the surface of the membrane it creates a shape where the top points of the wooden dowels are “anchoring� points of the mold. I tested the apparatus with rice before trying plaster.
1. In my first attempt I created a point in one plane and 6 point in another plane. I set one point and created a 1st degree curve from remaining points. Afterwards I connected those points with a line.
2. In my second attempt I created a point in one plane and two curves in second and third plane. I divided those curves and connected those points with lines. Change in divisions in one curve affects the number of connecting lines.
Using rice instead of plaster gave some incredible results. The membrane sagged profoundly but very elegantly under the weight of rice. Before the rice was added the surface of the membrane was completely flat whereas under about 2.5 kilograms of rice it sagged for about 15cm on points that were farthest from any anchorings.
Project One: Learn Learning From P-Wall by Luka Kreze
After testing the apparatus with rice I went on to using plaster. With every repetition I was closer to the desired shape, however I realised that for testing and form finding purposes using rice is much more suitable since it allows you to change the parameters during the test (weight of rice, arrangement of dowels, area of membrane) which is impossible with plaster.
FORM FINDING / RICE
6 dowels / anchors
3 dowels / anchors
Project One: Learn Form Finding / Rice by Luka Kreze
5 dowels / anchors
2 dowels / anchors
4 dowels / anchors
0 dowels / anchors
PLASTER MODEL CASTING Eventhough rice was more useful for testing how forces and elasticity influence the curvature, I decided to five a try to casting principle that Andrew Kudless used to create his P - Wall. The particles spread very evenly and the membrane sagged according to the arrangement and height of the wooden dowels. Result is much more pleasing to the eye than the previous failed attempt.
RUBBER + STRING
Project One: Learn Plaster Model
by Luka Kreze
DIGITALISING PNEUMATIC MEMBRANES SETUP First of all I created internal anchoring point (XYZ point) with fixed Z value and adjustable X and Y values (see Figure 2). Afterwards I added four corner points and limited their X and Y coordinates in 4 quadrants where each of the points gets a 10 unit maneuvering space in both directions, while Z value remains fixed (see Figure 1). I connected all four points with the anchor point, searched for the middle point and created a SDL line from all 4 middle points.
I used the end point of the SDL line as a Z limit for the surface of the entire structure. After joining points (corner, top, central anchor) into one set of points and altering their order, I connected them into a 2nd degree curve (see Figure 6). The end points of the SDL lines serve also as the middle points of the curves and always make sure that the curves are symmetrical. I lofted the curves (Fig. 2 and 7) and the result was a “pneumatic membrane structure� where all of the control points can be adjusted in order to change the shape.
Fig. 5: Definition
Fig. 1: Quadrant limits for the control points.
Fig. 7: Section
Fig. 3: Internal anchor coordinate settings
Using rice instead of plaster gave some incredible results. The membrane sagged profoundly but very elegantly under the weight of rice. Before the rice was added the surface of the membrane was completely flat whereas under about 2.5 kilograms of rice it sagged for about 15cm on points that were farthest from any anchorings. After testing the apparatus Fig. 2: Control points
Project One: Learn Digitalising Pneumatic Membranes by Luka Kreze
Fig. 4: Control points
Fig. 6: Close up look at definition for one of the curves
with rice I went on to using plaster. Since it dried very quickly I am still trying to find the right mixture. With every repetition I was closer to the desired shape, however I realised that for testing and form finding purposes using rice is much more suitable since it allows you to change the parameters during the test (weight of rice, arrangement of dowels, area of membrane) which is impossible with plaster.
FORM FINDING IN GRASSHOPPER
MANUAL TRANSFORMATION
SETUP Surface area = 1116mm2 (0,20)
(20,20) 7,5 Surface area = 747mm2 7,5
(0,0)
(20,0) 7,5
7,5
Limits: - Outer anchor points are limited into 4 quadrants (7,5 x 7,5 in size) so that they always remain surrounding the central anchor.
Fig. 1: Adjusting value of X (0 to 7,5)
Fig. 2: Adjusting value of Y (0 to 7,5)
Fig. 3: Adjusting value of X (20 to 12,5)
Fig. 4: Adjusting value of Y (20 to 12,5)
- Central anchor is fixed at (10, 10). Procedure: The lenght of translation vector is always 7,5 (quadrant limits). We begin with lower left point and shift it for 7,5 in X direction, we continue with points in counter clockwise direction and shift them for the same value in X and Y direction interchangably, as long as we reach all the quadrant limitations.
Surface area = 225mm2
Fig. 5: Adjusting value of Y (0 to 7,5)
Project One: Learn Form Finding in Grasshopper by Luka Kreze
Fig. 6: Adjusting value of X (20 to 12,5)
Fig. 7: Adjusting value of Y (20 to 12,5)
Fig. 8: Adjusting value of X (0 to 7,5)
FORM FINDING / GALAPAGOS / SHADOWS SETUP (0,20)
(20,20)
FORM THAT SUITS BOTH CRITERIA
Limits: - Outer anchor points are limited into 4 quadrants (5 x 5 in size) so that they always remain surrounding the central anchor when adjusted by Galapagos.
5
- Central anchor limited in a quadrant between points (5,5) and (12.5, 12.5)
5 (0,0)
(20,0) 5
5
Procedure: Shadow area was calculated according to the summer and winter sun angle in London, UK. Aim was to find a minimal summer and maximum winter shadow for the limitations stated above (Fig. 1 and 2). By using the F=X-Y function Galapagos has calculated which form would give best results in both summer and winter (Fig. 3)
Shadow area: 166mm2
Final result: Shadow area: 145mm2
Shadow area: 270mm2 Shadow area: 395mm2
Fig. 1 (above): Galapagos results for minimum summer shadows (note how the final result “dodges the 61.5 degree sun angle, London, UK) Fig. 2 (below): Galapagos results for maximum winter shadows (sun angle 14.5 degrees, London, UK)
Fig.3: Shape that within given limits achieves smallest summer and greatest winter shadow.
Procedure of setting up a function which allows Galapagos to calculate a shape which satisfies both of our wishes (see examples on the right hand side).
Project One: Learn Form Finding / Galapagos / Shadows by Luka Kreze
Shadow area: 840mm2 Shadow area: 462mm2
Shadow area: 1215mm2
Final result: Shadow area: 1997mm2
Maximum difference between summer and winter shadow area: -1405mm2 where summer shadow area is about 400mm2 higher from its minimal value from the previous test. The winter shadow area does not change considerably from the previous test.
SUMMER SHADOWS (London, UK / 21st June)
SHADOWS IN ECOTECT
The tested object is the result from the step before when by seting the limits (coordinates) I found a shape that casts minimal shadows in summer and maximum shadows in winter at the same time.
WINTER SHADOWS (London, UK / 21st December)
9AM
Project One: Learn Shadows in Ecotect by Luka Kreze
12AM
4PM
TREE MODEL 2 DEFINITION FOR 5 ITERARIONS
EXPLANATION
MODEL
My aim was to create a Grasshopper definition for a branching structure which would not require copying of four branches for every starting point in every level and that would let me control all of the branches with a single slider. Branching structure has a start in a single point which is moved upwards for Z. Z - value slider is fixed for every single story, however in every level the Z - value is divided by 1, 2, 4, 8 and 16 in 1st, 2nd, 3rd, 4th and 5th level respectively in order to make sure that the lines in everystory above are 2 times shorter than in the one below.
The shape below was transformed by adjusting the length of the Z vector. Every line lengthens proportionally by the same value, however in plan view the points stay in the same place since X and Y values were not altered.
The branches span into 4 quadrants with X and Y values of same absolute value but different sign (+, +; +.-; -,+; -,-). Those vectors are duplicated four times in every iteration in order to get four branches on every starting point and divided by the same number as the Z value (1, 2, 4 etc.) Every transformed geometry (point) in a single level is connected in to a set of points and is plugged in as a base geometry for the next level of branches to be moved upwards.
Project One: Learn Tree Model 2
by Luka Kreze
points with same name in other squares and I haven’t found a solution for that.
TRANSFORMATIONS
FIXED Z
FIXED X AND Y 1. Fixed X, Y / Z =40
2. Fixed X, Y / Z =30
3. Fixed X, Y / Z =20
4. Fixed Z / X = +-20; Y = +-20
FIXED Z AND Y 6. Fixed Z; Fixed Y / X = +20 to -20
Project One: Learn Transformations by Luka Kreze
5. Fixed Z / X = +-40; Y = +-40
TRANSFORMING
MEMBRANES AND BRANCHES
SHIFTING EXTERNAL ANCHOR
SHIFTING INTERNAL ANCHOR (X - DIRECTION)
DECREASING RADIUS OF THE ANCHOR
SHIFTING INTERNAL ANCHOR (Z - DIRECTION)
LOWERING OF THE MEMBRANE
SETUP Below is the initial setup of the membrane. External points and the internal anchor radius are limited by quadrants of 10 units, the position of the internal anchor is limited by a quadrant of 15 units. Any change of the branching structure affects the shape of the membrane, a change of the membrane does not affect the branching. (-15,15)
Shifting external anchor: X from 15 to 7.5 Y from 15 to 7.5
Shifting internal anchor: X from 0 to 7.5 Y fixed at 0
Decreasing radius of internal anchor from 10mm to 4mm by shortening branches.
Shifting internal anchor downwards from 5mm to 3mm by changing tree height.
Lowering the membrane by lowering curve midpoints from Z=30 to Z=20
Top view
Top view
Top view
Top view
Top view
Perspective view
Perspective view
Perspective view
Perspective view
Perspective view
(15,15) 7,5
15
7,5 (15,-15)
(-15,-15) 7,5
10
7,5
Top view of initial setup and limits (above)
Perspective view of initial setup
Project One: Learn Transforming Membranes and Branches by Luka Kreze
MODELING MEMBRANES / CIRCULAR ANCHORS
CHANGING THE RADIUS OF THE INTERNAL ANCHOR
SETUP
INFLATING A MESH / KANGAROO
Hypothesis: the higher the number of internal anchors, the lower the membrane is after inflation.
Below is the initial setup of the membrane. External points and the internal anchor radius are fixed while the radius of the internal anchor can be altered.
Procedure: I have created 3 meshes (size = 10 faces in X and Y direction, 1 face in Z-direction), each of them with a different amount of square holes (1 , 5 and 9). After inflating the meshes those square holes should become the circular anchors of the membrane.
Experiment on the right explores the relationship between anchor radius and the shape of the membrane.
Radius = 1mm
Result: After using a subdivision tool and inflating each of the surfaces (same pressure for each of them) the results were not perfect, the inflation is for some reason not precise, however, it did prove my hypothesis. Radius = 2mm
Top view of the membrane with circular anchor (above)
Section view of the with a circular membrane (above)
Project One: Learn Circular Anchors (Modeling Possibilities) by Luka Kreze
Radius = 5mm
Learnings: larger number of anchors does in fact result in lower membrane after inflation ( if the same pressure is applied to all the membranes)
MODELING MEMBRANES / ARCHES AND HEXAGONS AIM Every single control point needs to be an anchor. By distributing “external” control points in hexagons, adding a central anchor and connecting all the points with arches we get equilateral triangles inside the hexagons. External anchors of one units suddenly becomes internal anchor to another unit.
View from underneath the membranes (above).
Perspective view: 7 hexagons are joined.
Every point of every hexagon is an anchor 3 other hexagonal “units”.
Project One: Learn Modeling Membranes / Arches and Hexagons by Luka Kreze
MAXIMUM SURFACE AREA / GALAPAGOS
FINAL RESULT
SETUP B Point B (-15,15)
A
B
B
A
D
C
A
A
A
Point A (15,15)
B
B
7,5
15
D C
D
D
D C
C C
C
7,5 (15,-15)
(-15,-15) Point C
Point D 7,5
15
Galapagos progression 1: (plan view above, perspective view below)
Galapagos progression 2: (plan view above, perspective view below)
Galapagos progression 3: (plan view above, perspective view below)
Galapagos progression 4: (plan view above, perspective view below)
Galapagos final result (maximum area): (plan view above, perspective view below)
Point A: (12, 12) Point B: (-13.4, 13) Point C: (-14, -8) Point D: (10, -12.5) Radius: 2mm Radius center point: (0, 0) Height of circular anchor: 2,9mm Height of structure: 17mm
Point A: (12, 7.5) Point B: (-12.4, 14) Point C: (-14, -8) Point D: (12.5, -12.5) Radius: 2.5mm Radius center point: (0, 1) Height of circular anchor: 3.8mm Height of structure: 25mm
Point A: (13, 7.5) Point B: (-13, 14) Point C: (-15, -8) Point D: (14.5, -13) Radius: 3.2mm Radius center point: (0, 1) Height of circular anchor: 5.6mm Height of structure: 30mm
Point A: (13.5, 14) Point B: (-15, 14) Point C: (-15, -7.5) Point D: (14, -13) Radius: 4.2mm Radius center point: (0, 2) Height of circular anchor: 12.58mm Height of structure: 50mm
Point A: (15, 15) Point B: (-15, 15) Point C: (-15, -15) Point D: (15, -15) Radius: 5mm / 5mm Radius center point: (2, 2) Height of circular anchor: 15mm / 15mm Height of structure: 50mm / 50mm
Area of the surface: 1400mm2
Area of the surface: 1990mm2
Area of the surface: 2505mm2
Area of the surface: 4616mm2
Area of the surface: 5423mm2
7,5
Limitations: - External points and the internal anchor radius are limited by quadrants of 7.5 units - Anchor radius is limited to 5mm - Radius center point is limited by 2 units in all directions - Height of the circular anchor is determined by the height of branching structure and is limited to 15mm - Height of the entire structure is determined by the section curve midpoint and is limited to Z value of 50.
Hyphotesis: The greatest area will be achieved when corner points and structure height reach their maximum but the anchor height is at its minimum.
Project One: Learn Maximum Surface Area / Glalapagos by Luka Kreze
INCREASING NUMBER OF ANCHORS / COMPARISON OF PLASTER MOULDS
Fabric stretches profoundly with only two wooden dowel to hold it back. Difference in height between the anchor and highest point of the structure is about 15cm.
Number of anchor points: 2
Project One: Learn Increasing The Number of Anchors / Comparison of Plaster Moulds by Luka Kreze
By increasing the number of supports we get a greater number of curves with shorter length. This lowers the structure in areas with high density of anchors and slightly in areas with low density of anchors.
Number of anchor points: 6
Increasing the number of supports to a maximum of 12 gives us a very curvy surface where difference in height between the anchors and highest points of the structure is only about 4cm.
Number of anchor points: 16
BLACK ROCK MARKET
CIRCULATION DIAGRAM
INTRODUCTION Main entrance
Black Rock Market is structured around the idea of gifting. It’s phylosophy is not the one of buying and selling, neither any other form of exchange. It is based on the principle of simply bringing, giving and receiving goods, where value of goods is of no importance whatsoever.
Waiting area
Waiting area (example Superdrug festival bean bag area). Visitors need to respect that doors will open only when the airlocks are full in order to save energy and air. Hence waiting area needs to be provided.
Market consists of internal as well as external spaces, the main of which is the internal market area where goods are only displayed and up for grabs,without ‘sellers’ to control the goods. MARKET
There are three exist/entrances which act as airlocks. Each of these entrances opens at the same time and holds the same amount of people, depending on the overall voulume of the building.This means that when e.g. 20 people enters the building, 20 people exit. The journey, however, begins with the visitor “submitting the goods” at delivery gate. There is an waiting area infront of the main exit. What happens next is that at the exactly the same moment 20 people and their goods enter and 20 people leave the building. From the entrance visitor continues his journey to the market area to display his goods and choose the ones he needs. He can then enjoy these goods (in case they are drinks, food...) in the lounge area before exiting the building with his goods. Important factor in these transitions is the respect of scarcity ( goods, electricity and especially air). Transitions need to be efficient in order to for the cycle to function. Respect of the Black Rock Market’s Rules and Values is therefore extremely important. (see following sheet).
Visitors
Goods delivery
Market area (example Borough Market, London). Goods circulate without exchange of money. Here every one is a seller and everyone is a buyer, goods are priceless.
Goods Lounge
Campsite Stage
Exit
Project Two: Burn Black Rock Market by Luka Kreze
Lounge area (example chill out zone at Glastonbury). While listening to live music visitors can enjoy their eatable goods before leaving the Black Rock Market.
BLACK ROCK MARKET RULES AND VALUES MAIN PRINCIPLE
TANGIBLE / CONCRETE VALUES 1
GIFTING Gifting is the one of the ten principle around which Burning Man Festival is built. The value of the gift is unconditional and gifting does not contemplate a return or an exchange for something of equal value. In Black Rock Market goods are priceless. They have no value and all the value in the world. Exchange does not exist because exchange is only possible when goods are valued. Black Rock Market functions as a system where all participants believe that need is the only value. In a banal example this would mean that e.g. a car and a sandwich are of the same value just because someone might seriously need a car and someone else a sandwich. People are intrinsically good and they will recognise someone elses need.
Project Two: Burn Black Rock Market Rules And Values by Luka Kreze
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GENEROSITY (no generosity, no goods) Generosity refers to contribution of goods. Black Rock Market visitors are encouraged to contribute, however, those who don’t contribute are still allowed to enter and be gifted. It is believed that those visitors realize that system cannot work without contributions, hence, they will contribute next time.
INTERACTION (no interaction, no organization) Interaction refers to a dialogue between the visitors before and after entering the building. Visitors are encouraged to display their goods before choosing their own gifts, hence, visitors need to communicate in order to logically distribute goods / gifts. Communication is crucial when it comes to setting up and deploying the market, maintenance etc. PARTICIPATION (no participation, no market) Participation refers to physical engagement of the visitors in order to help run the market. Market is no mans property, it is only a tool which does not function without participation of everyone. This again refers to erection and deployment of the structure, its maintenance, distribution of goods, cleaning etc.
INTANGIBLE / MENTAL VALUES 4
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RULES AND VALUES DIAGRAM
DEVALUATION OF GOODS (no value, no money) In Black Rock market gift is unconditional. Money or any other sort of exchange is not accepted. One good is at the same time of the same value as one or ten other goods. We all have different needs an so in order to satisfy them we require goods which are never of the same value. In Black Rock Market this issue disappears. Need is the value, however, participants are not required to justify their needs. RATIONALITY (no rationality, no resources) Rationality is in a way similar to modesty, however it is more objective. It refers to a rational choice about number of goods someone will choose, time he will spent in the market etc. Black Rock Market is an inflatable structure, hence, not only the goods are scarce but also resources such as electricity and air. Awareness of the rational use of resources is crucial in order for the system to function. MODESTY AND EMPATHY It is believed that all participants of the Black Rock Market are intrinsically good people capable of empathy and that they are aware of the fact that every good they take means one less good for someone else, every breath means one less breath for someone else, every visit means one less entry for someone else as well as air loss.
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Main entrance
Waiting area
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3 MARKET
Visitors
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Goods delivery
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3 1 Goods
2
Lounge
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Campsite
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3
Stage
Erection and deployment. Exit
RESOURCES AND MATERIALS INFLATION
STRUCTURE
TRANSITION vs. AIR MANAGEMENT
ON SITE
ON SITE
ON SITE
WIND
SAND
CONTAINERS
Black Rock Market’s location assures constant wind around 15mph, with gusts up to 50mph. Wind can be an important resource when it comes to creating electricity.
Pneumatic membrane will have underground fixings and will be later covered with sand. This will provide not only extra support but also ach as a sealant.
Cargo containers will act as airlock spaces. When people enter the container one door opens and another closes which limits the air leak to only the volume of the container.
SELF MADE WIND TURBINE MATERIALS
TENSILE CABLES
By using scrap materials (plastic, timber, metal etc.) visitors bring to the festival it is relatively easy and cheap to build a home made wind turbine which creates op to 1000W.
Tensile cables will be used for internal anchorings as well external (depends on the required shape of the building.
AIR CIRCULATION SYSTEM
MEMBRANE MATERIAL
Since structure will be inflated only once (afterwards air will be pumped in only to replace the air lost by people exiting and entering and by ventilation) one of the options are relatively cheap bouncy castle air
Membrane material will need to have following characteristics: airtight (in one direction, in other perhaps not), semi transparency (for natural lighting), strength but also elasticity.
ON SITE
Project Two: Burn Resources and Materials by Luka Kreze
SMALL SCALE SAND EXPERIMENT
SETUP
Polyethene membrane is spread over the50x50cm box. Between the membrane and the base a straw is placed.
Project Two: Burn Small Scale Sand Experiment by Luka Kreze
To test whether sand alone can act as an anchor for inflatable structures 10kg of sand is spread over the membrane inside the box.
After inflation the membrane takes the shape whith suits it the most. (see following pages)
SMALL SCALE SAND EXPERIMENT INFLATION
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Project Two: Burn Small Scale Sand Experiment by Luka Kreze
SMALL SCALE SAND EXPERIMENT
Project Two: Burn Small Scale Sand Experiment by Luka Kreze