20 November 2011
STORM-WATER HARVESTING SYSTEM
Carolina Figueroa Song Pengfei Luis Hernan Preechayan Prapinwong
RAIN-WATER HARVESTING SYSTEM
Precedents ! Performative architecture!
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Deployable structures!
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Beyond parametric formalism—!
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Grasshopper in modeling performance!
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Context! Retrofitting the city through rainwater harvesting!
Performing architecture in grasshopper! Translating virtual into the real world!
Exploration prototype 1!
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Sand beast!
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Kinematics!
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Theo Jansen linkage!
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Implementation in grasshopper!
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Exploration prototype 2! Breathing bridge!
Actuated rain harvesting system!
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Final prototype!
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Stage 1—!
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Basic geometry !
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Stage 2—!
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Catchment surface lofting!
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Stage 3—!
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Actuation process!
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Further implementation!
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Conclusion!
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References !
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Precedents
Performative architecture Performative architecture is a broad term used to referred to a particular design approach holding performance in the same level as form-making. By using digital tools, designers are allowed to run performance-based simulation as to understand how built environment is affected by users and surrounding environment. There is a widely accepted statement linking performative volition in architecture to computational revolution. However, there has always been an entangled interaction between architecture, performance and culture. The performative turn in the 1950s involved a paradigm shift in anthropology and linguistic. According to it, every human interaction can be assumed as a ´performance´—a public presentation of the self— Culture started being looked at as “temporal processes defined by fluidity and mediation” (Kolarevic and Malkawi, 2005) In turn, architecture revolutionised to incorporate concepts of mediation and change. In 1963, architect and sculptor Nicolas Schöfer proposed the 323-meter high Tour Lumière Cybernétique in Paris (Figure 1). The tower would incorporate 260 mirrors, 3000 highpowered lighting instruments and react to wind, noise, atmospheric luminosity, and radio signals. (Salter and Sellars, 2010)
Figure 2 BIX, a “communicative membrane” by Peter Cook and Colin Forunier
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Figure 1 Project for Tour Lumière Cybernétique in Paris by Nicolas Schöfer
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Branko Kolarevic defines performative architecture as “having a capacity to respond to changing social, cultural and technological conditions by perpetually reformatting itself as an index, as well as a mediator of (or an interface to) emerging cultural patterns. Its spatial program is not singular, fixed or static, but multiple, fluid and ambitious� (Kolarevic and Malkawi, 2005)
Deployable structures The term deployable normally refers to a type of transformable structure that changes it size by actuating configuration changes. Generally, a deployable structure transforms from a compact phase to a large, deployable one. The first transformation is referred to as deployment, whilst the second is dubbed retraction. (Pellegrino and Sciences, 2001) Due to their particular geometrical traits, this type of structures is of particular interest to aerospace engineering since they offer an important potential for compact transportation. The main concept behind any deployable structure include the capacity to change configuration either via controlled deployment managed by a motor, or unconstrained development driven by stored elastic strained energy. The former involves a system of rigid bodies connected by simple mechanical joints. Nonetheless, the assembly shape is of utter importance in transmission of movement among members. Some of the simplest mechanisms include the umbrella. Further adding some complication, tensegrity structures can be arranged in assorted configurations to deploy foldable assemblies. Likewise, configurations derived from ruled-surfaces can also be arranged to create a successful deployable structure. (Pellegrino and Sciences, 2001) Some projects in architecture have found inspiration in deployable structures to yield responsive systems. Adaptive Shading Explanade’ by Chuck Hoberman generates active shading devices designed to respond to different conditions in environment. Similarly, other projects extrapolate the morphology of deployable mechanism into specific architectural; elements. The Al-Husayn Mosque Canopies by Bodo Rasch includes an actuated umbrella-like structure extending a shading surface. (Pawlyn, 2011)
Figure 3 Tensegrity sculpture by Snelson. Washington D.C.
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Beyond parametric formalism— Grasshopper in modeling performance Scripting has allowed designers a long-time denied capability—innovation— The more accurate description would the hypothesis—form follows software—As long as design is being yield by a predefined tool, question remains whether it is original or an iteration of a predefined process (Terzidis, 2009) Furthermore nature has served as a model to create formal analogies of flamboyant complexity “what is happening is the use of computers as marketing tools of strange forms whose origin, process, or rationale of generation is entirely unknown and so they are judged on the basis of their appearance often utilizing mystic, cryptic, or obfuscating texts for explanation” (Terzidis, 2006) Grasshopper is an object oriented visual programming language developed by David Rutten (Loomis, 2011) Publicly released in 2007, the visual environment allows designers to perform ‘spaghetti wiring’ scripting with virtually no background in computer sciences. The breadth of application the programme has reached is considerable, especially in the topic of bio-behaviours. For instance work by NBBJ , architectural firm based in Los Angeles, has proved to take advantages of robustness and flexibility offered by Grasshopper. In the project for Hangzhou stadium, they used grasshopper to define a parametric truss modules resembling the looks of petals based on loosely defined geometric rules. However parametric trusses are complicated on their own right, the real advantage comes into play when using Grasshopper to evaluate and optimise a pool of iteration to conform to structural, modular, material and programmatic constrains. (Miller, 2011) Notwithstanding, Grasshopper holds a yet to be explored potential for simulation and real-time management. Andrew Payne, doctoral student from Harvard Graduate School of design, has developed a number of projects and plugins to close the gap between the virtual limits and real world interaction. For instance, Firefly is a comprehensive plugin allowing Grasshopper to control and interact with Arduino micro-components. It also features a beta connection to Kinetic using Microsoft SDK. Nonetheless the greatest achievement in real-time data between physical and virtual worlds comes in the form of ‘A Five-Axis Robotic Motion Controller For Designers’ (figure 4), a research project also from Payne. Using the interface Grasshopper +Firefly+Arduino, the project connects a ABB IRB 140 robot to an abstract joint and axis abstraction running in Rhino. Moreover the project includes a Tangible controller for designers to manipulate the system via a physical interface. Grasshopper receives data input from sensors installed in the controller, translates it in rotation and displacement for Rhino-based model and generates instructions in Rapid to be fed into the IRB 140. (Payne, 2011)
Figure 4 Five-Axis robotic motion controller, by Andrew Payne
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Figure 5 Five-Axis robotic motion controller, by Andrew Payne. Grasshopper receives data feed from controller, modifies virtual model and generates Rapid script in real time.
Context
in actual application of techStudies—demonstrate the actual niques—such as the Seattle potential for water catchment Public Utilities Natural Drainage and reuse from rain storms and System—and in controlled stud- building equipment. Several ies. The University of Guelph in planned projects, and several Canada has found permeable currently in construction, are Rainwater harvesting refers to different methodspavers used to collect, store and conserve runoffsite of interlocking concrete designed to use all potential using any selection of structures and elements in thedemonstrate system.a 90 Nonetheless, recently the term blocks percent water for reuse or infiltration. reduction in runoff and One example of an in-conhas been used also to define collection of rain with some sortvolume of artificial inducement. that they significantly reduce 47 struction project is the Sidwell surface runoff pollutant loads. Friends Middle School located in Existing projects—as those D.C., a are building Benefits from using rainwater harvesting as a complementary source ofWashington fresh water selfdescribed in Chapter 5, Case designed to earn a USGBC LEED © Kinkade-Levario, Heather, Jun 01, 2007, Design for Water : Rainwater Harvesting, Stormwater Catchment and Alternate Water Reuse New Society Publishers, Gabriola Island, ISBN: 9781550923407
Retrofitting the city through rainwater harvesting
Rain-catching, shade-pr viding, upside-down umbrellas in a courtyar of multiple commercial office buildings Patio and stormwater swale below upsidedown umbrellas
HEATHER KINKADE-LEVARIO
Generally speaking, a catchment system includes up to six interconnected components: catchment area, conveyance, filter, storage, distribution and purification. To date, rainwater harvesting systems work in top of existing building or structures (Kinkade-Levario, 2007). Normally they comprise the use of downspout and gutters connected to residential roofs acting as catchment areas.
HEATHER KINKADE-LEVARIO
evident. Since rain is the direct and primary source for many water bodies, it provides high-quality, soft water. Moreover it reduces the need to pump and translate water from distant sources.
Figure 6 Rain-water harvesting system
Co
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Purpose-built structures for rain catching are referred to as rainbarns. (Kinkade-Levario, 2007). Some of these structures deploy their catchment surfaces only with rain, using some sort of deployable device. The Watree by industrial designer Chris Buerckner is “designed to bloom like a tree, this canopy of umbrella like structure expands out ward to capture falling rain” (Buerckner, 2011) A similar concept is followed in ‘Rainpod’ where the system incorporates a high placed tank to store and deliver water under pressure. (Hote, D. 2011) Changes in man-made environment have proven to increase water footprint considerably both in food production and direct consumption. As human population continues to grow, advances in ‘green revolution’ become more and more fragile as they are dependent on access to large quantities of irrigation (Pawlyn, 2011) Furthermore as temperature increases tropical latitudes are expected to experience a drop in rainfall, whilst risk of flooding rise in temperate regions. Figure 7 Design for ‘RainPod’ by Hote
Just as individual water footprint is expected to rise in years to come, some efforts has been made to shift dependence on blue water for atmospheric water. (Kinkade-Levario, 2007). Although some good examples in architecture hold natural system as metaphors in their performance, it is also abundantly evident the need for bespoken architectural solutions to address the challenge. The ultimate purpose for performative architecture is producing design solutions truly responsive to the environment, both natural and man-made. Then it is a natural evolution to respond to social changes and their impact on water demand. This research seek to understand extend and potential of connection between real and virtual worlds. Furthermore, it speculates on deployable structures to yield new paradigms in water collection and distribution. In the broader context of retrofitting the city, the final outcome of this research is an actuated rainharvesting deployable structure. When implemented, the structured will be connected to an underground storage facility, which will enable users to use the water in scarcity times.
Figure 8 Deployable umbrella strcutures in Medina, Saudi Arabia
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Following this train of thought, research question has been defined as
Can Grasshopper be used to simulate the performance of an actuated deployed structured for active rain-water harvesting?
Performing architecture in grasshopper Translating virtual into the real world
The greatest challenge to overcome involves translating mechanical movement to a set of mathematical rules suitable for Grasshopper scripting. Furthermore two discrete exploration prototypes were produced in an effort to achieve the more efficient procedure in defining mechanical movements. The final outcome incorporates the same logic as in exploration prototypes. The first prototype is dubbed “Sand-beast” and resembles a kinetic sculpture by Theo Jansen. Furthermore, the second prototype is focused at transmitting movement in a gear-based mechanism applied to a breathing cover for bridges.
Exploration prototype 1 Sand beast Kinematics Although there have been considerable attempts at feedback between real and virtual world, much of the efforts has been towards integrating hardware into Grasshopper. One key concept when dealing with simulation of real-world mechanisms is Kinematics. Kinematics is a branch of mechanics focused at specifying movement independent of any force beneath it. Using elementary trigonometry equations (Watt and Watt, 1992), movement is propagated throughout a system of rigid bodies. Each system is defined by a series of joints, and these in turn are defined through movement restraints or degrees of freedom (DOF). (Watt and Watt, 1992) The basic mathematical definition is as follows Depending on where movement is originated, the system uses inverse or forward kinematics. The simplest form of propagation is solved by forward kinematics. Given an initial condition of translation in the origin, translated coordinates in end effector are calculated using the equation
x = (l1 cosθ1 + l2 cos(θ1 + θ 2 ),l1 sin θ1 + l2 sin(θ1 + θ 2 )) However if movement is defined by translating the end effector, rotation transformation for and is calculated using inverse kinematics. The equations are as follows
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(x 2 + y 2 − l12 − l22 ) θ 2 = cos 2l1l2 −1
θ1 =
−(l2 sin θ 2 )x + (l1 + l2 cosθ 2 )y (l2 sin θ 2 )y + (l1 + l2 cosθ 2 )x
Theo Jansen linkage Jansen linkage is a planar mechanism emulating the animal walking movement by translating a rotational movement into an horizontal one. The system is comprised of 8 links, forming 5 moving joints and one fixed axis, and a connecting crank rotating counterclockwise. Consequently the length of rigid members determines the step height, stride length and ground clearance for the whole system. Theo Jansen started developing his system in 1990 using computational models to evaluate and refine configurations. His work has been mainly aimed at develop wind-propelled kinetic sculptures equipped with a mechanically-based artificial intelligence. The ‘animals’, as Jansen himself dubbed them, are capable of reacting to their environment via a mechanism involving air-pressured bottles and hosepipes attached to each leg. For the purpose of this research, the iteration commonly known as Sand Beast will be emulated in Grasshopper following kinematics principles.
Implementation in grasshopper Following forward-kinematics principles, the sand beast prototype starts off by defining a system of rigid bodies joined together by three degrees of freedom elements (figure 8)
Figure 7 Design for ‘RainPod’ by Hote
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Rotation around axis O, representing system crank, defines a transformation in coordinated for point A. Point D represents a fixed joint serving as pivotal point for the remaining system.
Figure 8 Abstraction from Theo Jansen linkage in Prototype 1—Sand Beast
When analysing equations for forwards and inverse kinematics, it becomes evident that the transmission of movement is abstracted to a correspondent change in angle for every rigid body. Therefore x,y coordinates for each point are defined as the correspondent trigonometrical function. Taking into consideration data flow nature in Grasshopper, the best strategy to translate kinematic principles was to define system joints through their position into a relative circle. In this fashion, grasshopper calculates trigonometric transformation natively, thus allowing the definition to only determine the connection rules among members. Following the principles found in Jansen linkage, the system is defined through one fixed and two translating circle. Translating circle 1 (TC1) revolves around point A whilst point C serves as centre for translating circle 2 (TC2). Fixed circle (FC) is drawn around point D. Some points base their transformation on a sector of a given circle, and serve to define changing coordinates for the rest. For instance, FC serves to control movement in point E. Points B and C are anchored to rotation in FC and transformation in TC1, whilst point G moves in a determined sector of TC2. The only element not defined by a circle is point F, which
Figure 9 Theo Jansen linkage in Prototype 1— Sand Beast. Definition is controlled by shown variables
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Figure 10 Grasshopper definition for Theo Jansen linkage in Prototype 1—Sand Beast
transformations are related to those in C and G. The remaining definition is an iteration of the above detailed process. Further, when connected in the whole system it proved useful to define general translation according to cumulative movement of elements. This first prototype proved a considerable efficiency of geometrical abstraction for simulating performance. Nonetheless, the more significant backdrop implied definition of ratio between radios for FC, TC1 and TC2 (Figure 9).
Exploration prototype 2 Breathing bridge
The prototype was created to simulate a wind-powered mechanical system for a bridge cover. The system is to transform rotation energy generated by a wind mill, connected to a gear system to finally activate a series of surfaces. When combined, surfaces generate an actuated cover forcing ventilation inside the structure. The prototype follows three basic operations—gear mechanism, transmission to extensile devices, and actuated surfaces. The gear mechanism phase is responsible for rotation transmission from wind mill to a gear mechanism ending up in a transmission axis. All components are connected to the same slider, simulating the actual force of wind. (figure) Rotation in wind mill is directly connected to rotation in Gear 1, thus determining the acceleration in angular speed. However, speed for Gear 2 and 3 is determined through the following function
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WindSpeed × rg1 rg2
Where rG1 represents radius for analysed gear and rG2 stands for radius of next gear. In phase 2, the definition transforms rotation inherited by gear 2 to a linear displacement through an extensile device. Each extensile device is comprised of two parts-a circular component (CC) inheriting rotation from gear 2, and a linear component (LC) translating rotation into linear movement. (figure)
Figure 9 Theo Jansen linkage in Prototype 1—Sand Beast. Definition is controlled by shown variables
CC and LC are divided in n segments, generating the same amount of n lines. The system translates movement as a boolean variable in each line. As a general rule, two lines cannot have the preview value set to true at the same time, and once turned on it will inherit the value to the next element whilst shutting down. Each of the segments in LC represents a ‘top point’ forming the cover of the bridge. As values are inherited in the cycle aforementioned, top points will shift to form the cover surface. Each time a boolean changes its value, the system will calculate the surface again, generating the movement in the mechanism.
Figure 10 Exploration Prototype 1—Sand Beast.
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RAIN-WATER HARVESTING SYSTEM Figure 11 Prototype 1—Sand Beast. Definition for extensile device
Figure 12 Prototype 1—Sand Beast. Complete definition
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Actuated rain harvesting system Final prototype
Figure 13 Final prototype—Actuated rain harvesting deployable system
Considering the challenge of urban and rural rain harvesting, the proposed solution involves an actuated system following the principles of deployable structures. In a performative level, it is comprised of two actuated elements— catchment surface and supporting structure—
Following an initial exploration on the topic, purity in collected water was identified as one of the most significant yet unmanaged challenges. Current recollection system depends on collecting runoff from a designated surface. Nonetheless if water is intended for human consumption systems ought to include both filtration and purification phase. Captured rainwater quality depends upon a manifold of factors, including air quality. However, runoff surface significantly increases risk of contamination. Nowadays harvesting system relies on smooth surfaces, rainfall pattern and frequency to influence cleanliness of catchment area. The proposed system tackles this eventuality by actuating the catchment structure. When a series of sensors deployed near the structure detect enough moisture in the environment, the system will deploy both the structure and catchment area to initiate harvesting process. Once the system interprets a significant drop in catchment potential, the structure closes as to isolate catchment area from any pollutant transmission from environment. Combined with rainwater acidity, quality of recollected water is significantly better than in traditional systems, hence minimising sophistication required for filtration and purification.
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Figure 14 Final prototype definition. Stage 1 in green and stage 2 in red. Stage 3 depends upon connections
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In this paper the logic beneath the Grasshopper definition will be analysed in three stages: basic geometry, catchment surface lofting and actuation process
Figure 15 Evolution for stage 1. Components created in different steps
Stage 1— Basic geometry According to the brief, the system should be self-supporting and avoid the need for a secondary structure to be activated, as it happens with umbrella-like structures. Hyperboloid structures demonstrated to be structurally sound, and due to its ruled surface nature suggested an interesting potential to be integrated in a deployable system. One way to define an Hyperboloid is by generating lines which in turn creates the ruled surface. Therefore, two circles were defined representing hypothetical rings formed by starting and ending points in the ruled surface. Curves were then divided creating 23 point in each one (Figure 16). In Grasshopper, geometrical shapes are treated as ordered sets of data. When a circle is divided, the corresponding data array is expanded by the specified number of instances. Simultaneously trigonometric calculation are natively carried out to define (x,y) coordinates to populate the array.
Figure 16 Definition of base circles
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Consequently points in circle are connected through lines using a shifted array of point (figure 17). In order to attain a structurally sound shape, a lattice structure is defined by connecting each point to a two-point set in the opposite end. Therefore, a definition for connecting both arrays of points is carried out twice and piped to connect lines in opposite directions.
Figure 17 Lines are created by connecting a shifted array of points
Figure 18 Lines are used to define several circles which will serve to build the catchment surface of the system.
Figure 19 Evolution for stage 2. Components created in different steps
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Stage 2— Catchment surface lofting The progression from the starting shape to enlarged final form is managed by actuating two interrelated systems—supporting structure and catchment surface. Nonetheless, they have to be defined separately as catchment surface is to close completely to remain sealed to pollutants in environment. Lines created in last step are now used to define several circles which in turn serve to build a catchment surface for the system (Figure 18). Each line is divided in six segments and stored as a multi-dimensional array inside the divide component. Using a param-viewer component, it is possible to visually understand data storage in two levels. A First-level component represents an array of points in the same z coordinate but corresponding to one of the discrete array of 46 lines. The multi-dimensional array is mined by retrieving six first-level components. Later on, these components will constitute lofting reference circles. Then each first-level component is broke down in three further-level components to generate a total of three points. In turn these points define a circle. Since catchment surface is housed inside the supporting structure, the definition should resolve any overlapping by applying a hard-coded scaling factor for reference circles. Notwithstanding, some of these hard-coded scaling factor have to be replaced by a mathematical function defining a faster rate in closing catchment surface.
Figure 20 The multi-dimensional array is mined by retrieving six first-level components. Later they will constitute lofting reference
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Figure 21 To avoid overlapping, hardcoded scaling factors are applied to each circle
Figure 22 Variable closing ratio for catchment surface attained through mathematical formula
Stage 3— Actuation process Varying the diameter for base and bottom circles creates the basic process in deploying the structures to its final shape. However, two complications arise. When dealing to real-world events, abstraction ought to consider material implications. If the system is solely defined through the position of discrete points relative to a set of abstract circles, rigid bodies ‘elongate’ their length as a consequence. The second challenge is to implement an integral control of the system, whilst maintaining a separate ratio in contraction for each element. In an effort to solve the elongation problem, it was concluded that z coordinate for upper basecircle should be affected as a function of change in diameter. Therefore a dynamic function is plugged to z vector in upper base-circle, and further connected to change in bottom basecircle diameter.
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As catchment surface and structure initial shape differ, diameter for both base-circles must be connected yet remain independent in their progression of values during deployment. It was determined that the best way to attain a variable ratio was to affect input values by a trigonometric function.
1− (cos((
d1 d1max
* 3))
Where d1 represents diameter for base circle and d1max is the highest possible value for basecircle diameter when structure is fully deployed. Then resulting values are fed into diameter parameter for actuating catchment surface defining circles. (Figure 22) Propagated effect in surface performance is a soft deployment progression ending in a completely sealed shape.
Figure 23 Deployment of structure in different stages
Further implementation As defined earlier in this paper, the optimal stage in performative architecture involves a twoway feedback between real and virtual environments. When analysing webpages and forums showcasing Grasshopper projects, it is clear that the platform is being extensively used in parametric design. However, this paper posits there is still a great potential for simulating performance. Furthermore, analysis in how structures behave in real-world can impact on their design and redefine performative architecture in common design packages. The final outcome of the software prototype, in terms of data structure, is an array of coordinates corresponding to defining points in the system. A further iteration, corresponding change in coordinates could be used to generate and translate code using firefly for grasshopper plugin. This would enable the definition to translate grasshopper commands to an actuator using native language such as G-code. Also, slider changing diameter can be substituted by sensors monitoring ambient humidity.
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If implemented in real scale, the system will help to shift paradigms in terms of recollection and distribution of water. A cluster of actuated rain harvesting deployable structures will help to tackle water shortage in a community level. Each community will be able to recollect and store its own reserve, and as system optimises quality water is fitted for human consumption with little filtration steps. All the same the system will be specifically beneficial for developing countries and rural areas, where water has become an urging matter. Figure 24 Contracted structures integrated in context
Figure 25 (below) Implementation of structures within context
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Figure 26 Deployed structures working in context
Figure 27 (below) Deployment of structures in different stages
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Conclusion Work in this research yielded conclusions that are applicable to a general sense when dealing with performative architecture. Whilst IK is a mechanical concept widely implemented in computing processes, it is commonly ascribed to animation and robotic simulation and control. Implementation in commercial CAD software, such as Maya, Cinema 4D or 3DS Max, include animation tools to create skeletons. By assigning joints and rigid-elements properties to existing geometry, natural movements can be emulated by controlling position of end-effectors. In grasshopper, there are currently two plugins to emulate IK in parametric design—Kangaroo and Lobster IK—. Kangaroo is a live physics engine aimed at creating interactive simulation. On the other hand, Lobster IK and allows users to simulate and control 6 axis-based systems, mainly zeroed at controlling external robotic devices. Although both of them are quite useful, they are more fitted for robotic applications rather than performative structures. Results in the three software prototypes presented suggest that an efficient way to simulate performance is by abstracting mechanical principles to a set of mathematical formulas and representations. Coupled with the streamlined process in trigonometric calculations built inside Grasshopper, systems perform in a fairly efficient manner. As refined through evolution between prototypes, the more efficient framework to simulate performance of structures includes three main processes: basic geometry, overlapping considerations and implementation of actuation mechanism. Furthermore Grasshopper proved to offer a stable and reliable platform for performative architecture. During test and even with the integration of the whole system, the system performed extremely well in different hardware configurations. There is no doubt Grasshopper can be further used to control the system in real-time. Latest builds in Firefly plugin for Grasshopper open a wide potential area for development in attaining the two-way feedback between man-made environment, natural environment and virtual world.
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References KINKADE-LEVARIO, H. 2007. Design for water : rainwater harvesting, stormwater catchment, and alternate water reuse, Gabriola Island, B.C., New Society Publishers. KOLAREVIC, B. & MALKAWI, A. 2005. Performative architecture : beyond instrumentality, New York, Spon Press. LOOMIS, M. 2011. About Generative Design platforms. Available from: http:// designplaygrounds.com/deviants/about-generative-design-platforms-by-mark-loomis/ [Accessed November 11th 2011]. MILLER, N. 2011. NBBJ: Parametric Strategies in the Design of Hangzhou Stadium (Part 1) The Proving Ground [Online]. Available from: http://nmillerarch.blogspot.com/ 2009/12/parametric-strategies-in-design-of.html [Accessed November 11th 2011]. PAWLYN, M. 2011. Biomimicry in Architecture, RIBA Publications. PAYNE, A. 2011. A Five-Axis Robotic Motion Controller For Designers. Available from: http://vimeo.com/30237148. PELLEGRINO, S. & SCIENCES, I. C. F. M. 2001. Deployable structures, Springer, c c2001. SALTER, C. & SELLARS, P. 2010. Entangled: technology and the transformation of performance, MIT Press. TERZIDIS, K. 2006. Algorithmic architecture, Amsterdam ; Boston, Architectural Press. TERZIDIS, K. 2009. Algorithms for visual design using the Processing language, Indianapolis, IN, Wiley Pub. WATT, A. H. & WATT, M. 1992. Advanced animation and rendering techniques : theory and practice, New York, N.Y. Wokingham, England ; Reading, Mass., ACM Press ; Addison-Wesley Pub.
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