A Physical Costa Surface 3/3: Building the structure

The fabrication of a tensile structure is a complex design process. How can the mathematical shape and the form found geometry derived in the first and second parts of the series be used as the basis for a sculpture? In this final post of the “Physical Costa Surface” series, the Costa Surface sculpture takes shape.

The dimensions of the sculpture are 1.5m of height and 2m of diameter. In order to build the sculptural installation, four steps are necessary: patterning the surface, designing the interaction between compressive and tensile elements, cutting the fabric and assembling the pieces.


Thread direction in fabric – the warp direction is often prestressed during manufacturing

The first task to making this surface a physical reality is patterning. This operation is maybe the single most important in the design process. The success of the patterning will in part determine if the tensioned surface will wrinkle or not. Fabrics used in engineering projects have generally a high level of anisotropy with warp and weft directions of the weave determining the material properties. In loom manufacturing, the warp direction is generally pre-stressed while the weft is weaved. In our case we used a high quality nylon/spandex fabric presenting a four-way stretch (ideally equally stretchable in warp or weft). The fabric can accommodate large strains so the risk of wrinkling is minimized.

We performed the patterning on the initial mesh geometry of the form finding procedure (details can be found here). In this process three distinct patterns are produced. The figure below shows how the patterns are distributed over the surface. The patterns are shrunk to compensate for the pre-stress and large strains in the membrane.

Patterning of the 6-hole Costa surface

Interaction tensile / compressive elements

The visuals of the structure have been so far limited to the surface itself. The constraints of the mathematics are fixed boundary conditions. The constraints of the fabric impose the application of the tensile stresses. These will in turn modify the position of the boundaries.

In order to create rigid circular boundaries, 3/8in. (9.5mm) glass fiber reinforced plastic rods were used. They were bent into 1.5m  (top and bottom) and 2m (center)  diameter circular hoops and connected by aluminum sleeves (ferrules).

The top and bottom rings are equilibrated by bending active GFRP rods. As seen in the figure below, by being bent, the rods push the two rings apart. The actions of the rods are equivalent to the thrust of an arch, providing the necessary force to achieve a height of 1.5m as specified in the computational model.

Building the sculpture


Graduate Student Xi Li with the initial Paper Model

A relatively large scale (1-2 meters) was chosen for ease of fabrication, thus a large quantity of fabric was required to produce the final product. Before handling the fabric however, the final patterns were cut on paper and a smaller scale paper model was created. The paper model served two important purposes. First, assembling the paper model provided insight into the most efficient sewing sequence. Since the model was to be sewn entirely by hand, arranging a way to avoid attaching fabric pieces at awkward angles given the constraints of the sewing machine was crucial. Secondly, the pieces of the fabric model were labelled and served as a “map” during the sewing process to keep track of the pieces of fabric (24 total).

After successfully constructing the paper model, MDF patterns of the three patterns at full scale were lasercut. The final patterns were adjusted to accommodate seam allowances for attaching edges, and allowances for sleeves to hold the rods that would form the three rings. The MDF templates were used to trace the patterns onto the sheets of fabric, and were cut out by hand. The pieces were carefully sewn with a commercial sewing machine in the sequence below.

Sewing Sequence

Once all of the pieces were properly attached, the fiberglass rods were inserted into the pre-sewn sleeves to create the rigid circular boundaries. As they were inserted, they were connected with specially designed, 3D printed connectors in order to insert six additional bending-active rods to push the top and bottom rings apart. Once the buckled rods were inserted, the Costa Surface model sat at the design height of 1.5m, fully tensioned with no wrinkles.

Built structure

Final Model (Whole)
Fully Assembled Costa Surface
Final Model (Buckled Rods)
View of Buckled Rods and Connectors
Final Model (Whole) 2
Finished Sculpture

Author: Victor Charpentier and Tracy Huynh

Designed and Produced by: Xi Li, Victor Charpentier, Max Coar, Tracy Huynh and Olek Niewiarowski, graduate students at Princeton University


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