Luigi Olivieri, who is visiting the Form Finding Lab this week from the University of Tre (Rome, Italy) with Professor Stefano Gabriele, presents his master’s thesis work: The project explores the possibilities of using the hygroscopic proprieties of wood as a programmable material. The aim of the research is to explore the possibilities of a temporary structure through a new method of design by studying … Continue reading HIGROW – Hygroscopic proprieties of wood used as programmable matter in lightweight construction
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.
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.
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
The second Saturday of May is National Archery day (May 14 in 2016). While today archery is mostly practiced for sport, the bow and arrow have been used by humans in hunting for centuries. The purpose for bows, regardless of the target, is to propel an arrow using stored elastic energy. They are one of the most effective ways of storing energy of the human muscle.
The oldest bow in one piece dates back to 800 BC, the same era that scholars believe Homer’s Odyssey was written. The Odyssey tells the journey of Odysseus, a hero in Greek mythology. As part of the story, his wife, Penelope, patiently waits for 20 years during and after the Trojan War for her husband to return. Through this time she challenged her suitors to string the bow of Odysseus. With the exception of Odysseus himself, none of the suitors possessed the strength needed to string the bow.
While Odysseus was a Greek hero, there is a limit to human strength when stringing a bow. The human body allows one to draw their arm back about 60 cm and the maximum force a strong man can withstand holding in a string is about 350 N (Gordon). Therefore, the available muscular energy is 0.6m*350N= 210 Joules. Assuming an unstrung bow has zero energy, we can linearly plot the force from the archer’s pull against the maximum extension of the string in Figure 1. The energy stored in the long bow is equal to the area under this plot (triangle ABC): ½*0.6m*350N=105 Joules. This stored energy due to deformation is known as strain energy.