As Hurricane Dorian made landfall, we are working on inflatable barriers that could protect coastal cities from storm surges in the future.

This  Blow-up Bulwark article was originally published on November 2, 2017 on Urban Omnibus We associate inflatable structures with ludic landscapes like the bounce castle and hippie hangout. Impractical techno-utopias all. But for engineer Sigrid Adriaenssens and her Form Finding Lab, inflatables could offer a very practical response to the growing threat of storm surge flooding and the uncertainty of climate change. More air bag than … Continue reading As Hurricane Dorian made landfall, we are working on inflatable barriers that could protect coastal cities from storm surges in the future.

How to describe the esthetics of structural surfaces? (2/2)

In an earlier post, I wrote about how and why we seem at loss for words when describing the esthetics of a structural surface. I continue that discussion here and analyse what vocabulary layman use and make suggestions for where we might seek additional jargon. I  build my argument upon the results of an experiment carried out by graduate student Rebecca Napolitano in Fall 2016 on the Princeton University Campus.  In the physical experiment, a membrane was installed on a highly frequented location on a central location next to a neo-gothic medium size building.The  membrane was shown in an existing built environment, which might have caused distraction from observing the pure membrane form, but allowed for a full 3D perception of the membrane deforming in the wind.  Randomly selected 138 undergraduate students who passed by the installation, were asked to describe the membrane structure with one word.  If their response coincided with an already recorded word, they were prompted for another defining word.

This physical experiment yielded a plenitude of words which can be catalogued according to formal analysis or subjective response classes. The first category, formal analysis, is grounded in the fine arts and Vitruvian architecture tradition. This type of analysis disassociates itself from reactions such as elation, fear and awe.  These words describe emotions or subjective responses and constitute the second category.  The subcategories in both classes were pre-established before the collection of data and are based on the ones discussed by [1].

Formal Analysis

We first investigated the vocabulary pertaining to the category of formal analysis. This category holds the subcategories of form, proportion, space and visual mass.

Observing the 3D form of the membrane is not a simple process. In the past, built form has been discussed as a hierarchy of simple forms combined according to rules, into an assembly of complex forms [2].  The words in the experiments refer either to the simple or the complex form or the rule.  Simple form descriptions in Rebecca’s experiment included words such as “round”, ”bulbous”.  Complex form descriptions included  “nurbs”, ”free form” and rules included “tangent continuity”, “cambered”, “periodic”, “smooth”, “logarithmic”, “interlacing”, “weaving”, “optimized” , ”linearly disruptive” and “bendy”.

Nurbs, non-uniform rational basis spline (image credit

The subcategory proportion evaluates the geometric relationships between the different parts. Traditionally formal rules for proportioning have been defined buildings composed out of analytical forms including hemispheres and cylinders. Unfortunately, they are not that relevant for force-modeled systems such as the membranes in the experiments, because these membrane geometries are far more complex.  These geometries are generated by the laws of physics and are more difficult to proportion and steer than analytical ones.  A few words like “contrived complexity” hinting at these characteristics, showed up in the experiment.

A number of words in the experiments related to space.  The observers understood space as the Aristotelian idea that the membrane created both a positive space and a negative space or “embrace and grows space”. Words like “encompassing“ (positive space, the membrane itself) and, “limitless” and “unconstrained” (negative space, the space that co-exists separately alongside the space occupied by the membrane itself) exemplified the subcategory space.

Visual mass as opposed to actual mass can be achieved by the perceptions of light, color and texture. The untrained observer tends to make a connection between visual and gravitational mass.  Previous studies show how white surfaces, such as the one in the physical experiment, and the smoothness of the membrane in the experiment helped the structure as being perceived as lightweight [1] . These perceptions were captured in the experiments in the words “sinuous” and “slim”.

Subjective Responses

Besides the words that fall in the category of formal analysis, we closely examined the second category, called subjective responses. The results showed that the observers felt that the membrane has a certain character that spoke to them.  The words were distributed over the subcategories anthropomorphism, sensuality allusion, physical security and empathy.

Some observers saw the membrane as a living creature (eg. “sting ray”, “cocoon”) and endowed it with personality and intent. This association is called anthropomorphism.  The membranes were also perceived as “pregnant in the breeze”, “in bloom” and “about to take flight”.

Many observers found that these surfaces had a sensuous quality and captured those impressions in words like “sensual”, “voluptuous” and “calliphygian”. These words refer to the movement of the membrane as it progresses to a visual climax, followed by a relief of tension. In particular the inward and outward curving membrane surfaces have a particular sensual quality, which is missed by forms with single curvature.

Some spectators covertly or indirectly referred to an object from an external context.  The membranes evoked allusions with words such as “Rubenesque”. This word for example refers to the works of the Baroque painter Pieter-Paul Rubens (1577-1640) and means plump or rounded in an attractive way.  Other images included poetic metaphors such as “symphonic”, “motion frozen in time”, “essence of motion”, “natural choreography”.  Other allusions included scientific, artificial natural associations such as “meniscus”, “satin/silk, “hilly” and “motion of water”. These references to physical objects, although they are not grounded in the innate perception of the observer, contributed to aesthetic experiences while viewing the membrane.

Anthropomorphism, an association to a sting ray (left ), allusions to Ruben’s works (right), ,silk (bottom right) and hilly (bottom left) call the membrane in the wind to mind without mentioning it explicitly. (image courtesy Flickr the Commons)

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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

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A Physical Costa Surface 2/3: Form Finding Process

How can we algorithmically approximate the form of the mathematically defined Costa surface? This question is at the center of this second blog post of the “physical Costa surface”series. The form finding approach introduces a physical dimension to the equation generating the minimal surface. Finding the shape can be done in several ways. However, whether it is physical form finding or numerical form finding, the … Continue reading A Physical Costa Surface 2/3: Form Finding Process