Nets can be planar or extend spatially. Three-dimensional net arrangements cannot simply be unrolled, and thus need to be made in a different manner than planar nets. Current computational tools for formfinding planar nets are not very well suited for form-finding more complex spatially extended nets. Computational form-finding methods for nets and membranes exist in the form of dynamic relaxation, an iterative process which calculates and updates geometry step by step towards the eventual equilibrium state, yet requires careful modification for the purpose of form-finding complex spatial nets. For the purpose of designing spatially extended nets, different methods need to be devised that may also hold the potential of integrating design and engineering methods. Spatial nets can for instance be articulated through a branching logic. Such a branching cable net was developed for the Emergent Technologies and Design End of Year Exhibition in 2005 at the Architectural Association. The net starts from a singular point at the floor and branches into three sets of cables that develop per pair along individual trajectories. This branching cable net is triangulated for the sake of enabling direction changes in the net and thus forms planar fields between the triangulations. These fields are populated with circa 800 tetrahedral components that are transparent and coloured in order to modulate the luminous environment of the exhibition space. The branching logic and direction of the cable net is of key importance with regard to orientating the components in a defined way towards the light source. A second cable net was designed and built for the Emergent Technologies and Design End of Year Exhibition in 2008 at the Architectural Association as part of the MArch Dissertation of Sean Ahlquist and Moritz Fleischmann, delivered in February 2009. This net is defined by the network topology, which consists of computational springs through which form is generat ed by finding the equilibrium state of tension forces. The network topology is based on a ‘ring’ network method of association. Manufacturing and assembly constraints are embedded within this setup. Part of the potential for the network

topology is to realise a specific architecture of multiple spaces defined by a single continuous boundary. Through a series of initial experiments a net based on an involuting cylinder is derived. The circular array of anchor points undergoes transformation into an elliptical array. It is then varied and tested to determine which end-nodes of the system attach to points along this elliptical array. A node is the point at which the springs connect. The spring, in the relaxed model, defines a physical distance between the nodes. The variable of switching nodes from being fixed to un-fixed was tested for various locations. This served to investi gate the ranges of density in the resulting mesh and the number of required anchor points. Fabrication is a matter of coordinating this information and qualify ing it to the characteristics

of the intended material. This logic is universal in the system. Whatever the formal outcome is, the method for sorting through the nodes for fabrication is the same for each result. The node identification is the most valuable information of the entire system. The next step is to understand the sequence of connecting the nodes. The selected cylinder topology is of particular interest because it describes a boundary and directionality. In a form-finding process, these spatial characteristics can also arrange structure. This possibility of organising space together with structure is a key characteristic of the installation. A membrane component serves to articulate the flow of views and space between the two meshes of the net instal lation. Compression elements exist in the computation al model to push the surfaces

4320 1 0 1 8

01 0124 3 4 3 11121315 1014

of the net apart in specified regions to modify spatial characteristics. In construction, they also serve as a device for post-tensioning. The research for the installation focused on how to construct and associate a series of interconnected cylindrical nets that were comparatively autonomous. When beginning to associate multiple nets, the need for hierarchical arrangements arises, so as to manage a growing number of elements, arrays and variables. Thus the attention shifted to the topology of the spring networks, as opposed to discreet geometry, in turn requiring a computational method that is extensi ble to be able to facilitate the generation of topologically varied cellular pattern. The

cellular network was generated through a subdivision algorithm that was created in RhinoScript (see Chapter 1). Configurations were generated in which the complex net resulted in a branching arrangement. The latter is not directly coded in the script as a ‘branching’ function. It merely emerges because of a specific arrangement and accumula tion of coincident points and edges. Recognising this relation in the process helps to qualify some of the geometric definition in the cellular framework mechanism of the system, and the subdivision algorithm that drives it. There are three main conditions that arise: [i] frames that associate with the context and create fixed anchor points; [ii] frames that

only define association between neighbouring nets; and [iii] frames that are a hybrid of both – association and location. This setup begins to expose the ‘meta-spring’ aspect of the system. Here, it expands beyond a device for connecting to anchor points. Instead, it becomes a larger network of springs which aids in controlling the overall form of the net. Setting up design tests for such methods is a crucial element in their development. A second design elaborated through these methods was the design for a bridge with four cylindrical branches that constitute an inhabitable space at their intersection. This net too was utilised to act as a frame for an array of membrane patches to result in a greater degree of enclosure of the space of the bridge. Again this demonstrates the integration of spatial and structural aspects in the form-generation setup. A second design for a net-bridge was developed in the studio and constructed at Hacienda Quitralco, in Chilean Patagonia, in 2008. The scheme consists of two sets of ropes that are interlaced and rotated in such a way that a hyperbolic paraboloid results with its arching curve along the long axis of the bridge. In order to address the unknown soil conditions, the arrangement of the four poles of the bridge was deliberately chosen to be asymmetrical to suit different arrangements. With the bridge not depending on a symmetric arrangement, poles could independently be shifted in location in response to given soil conditions. Once the design strategy was established, crucial solutions for low-soil-impact anchor-points for the tensioned ropes and integrating the decking into the scheme needed to be developed. Detailed scheduling of the assembly procedure and knotting and lashing procedures finalised the construction document. After purchasing rope, belt ratchets for tensioning and some essential tools in Santiago de Chile, the Emergent Technologies and Design group travelled to the remote site in Chilean Patagonia. Upon arrival all sixteen holes for the anchors and poles were dug; the poles and anchors were prepared and placed; and the holes were closed and the soil compacted. The distance between the poles on either side of the river is circa 20 metres and the distance

between the furthest anchor points is circa 40 metres. The ropes and spacer-beams were assembled in a nearby barn, carried to the site and installed. Then the crucial pre-tensioning phase began, while the decking was prepared. After the decking was placed, the post-tensioning phase began. With the use of the belt ratchets and slipknots, the ropes were tensioned. Not all ropes could be tensioned simultaneously owing to the low number of available ratchets, which resulted in disequilibrium of tension in the overall system during the process of post-tensioning. However, this was counteracted by careful sequencing of the post-tensioning process. As the tension increased, the knots securing the ropes began slipping and different knots needed to be deployed. Eventually the rope began to stretch more than expected, with its diameter dramatically decreasing, at the point of which the tensioning had to be stopped as the knots began slipping again. However, the tension at this stage was sufficient and the project completed two days ahead of schedule. Research into complex spatial nets and also into the construction of such systems in a context with few anchoring options or lack of high-end technology is one of the key research areas of the Emergent Technologies and Design programme, as these systems have the potential to be used as supplementary architectural interventions in, for instance, climatic contexts where intermediary spaces between fully climatised interiors and fully exposed exteriors do not exist. With fast-to-assemble lightweight systems, such intermediary spaces can swiftly be provided together with an advanced passive environmental modulation capacity.