In the Barry Onouye architectural studio at the University of Washington, we are exploring how nets can be imagined and built for visual expression. In my previous post, we discussed the mechanics of nets and exemplified their behavior with nets that we use in daily applications. In this post, we turn our attention to how net can be topologically classified and how we see those topologies in nature and art (or more specifically art). In some of the instances shown, the arrangement of disconnected cables make an invisible form visible. I will be using sketches from the 2015 Pritzker Architecture Prize winner, Frei Otto recorded in the IL8: Nature and Technics, choreography images collected by the choreographer Rebecca Lazier (more about this phenomenal person later) and pictures from nets that occur in nature.
A planar network of cables or ropes can create a vertical surface. For example, this configuration occurs when vertical cables are connected to a suspended cable like in a suspension bridge. These connections could be branched or supported from intermediate shorter cables to ensure a more uniform deformation for a suspended track wit a moving load.
Freely suspended individual cables can create the illusion of a curved surface, which can be either zero Gaussian anticlastic or synclastic depending upon the form of the fixed boundary conditions. Equal length cables suspended between two horizontal lines, generate zero Gaussian surface (ie in the one direction the cross-section of the imaginary surface is a catenary, in the other direction it is a straight line. Replacing the two horizontal lines with arches or suspension geometries, the imaginary surface becomes anticlastic or synclastic respectively. By just changing the boundary conditions (horizontal lines to arches of suspension geometries), an amazing array of different imaginary surfaces can be obtained. The architects Ryuji Nakamura exploited this minimalist geometry for their installation bench between pillars.
Other interesting imaginary surfaces occur, when simply suspended cables are arranged radially. Cables suspended at regular intervals around a horizontal ring, generate an imaginary cylinder. But when all free ends are connected to one point, a catenoid arises. A catenoid is a figure that results form rotating a catenary curve about an axis (and is a minimal surface). Interesting imaginary forms arise from this seemingly minimalistic configuration when 1) the horizontal ring rotates about an horizontal axis, 2) the connection point is displaced in 3D space, 3) the connection point is replaced with a circular ring or 4) the boundary is no longer a ring but an arbitrary planar curve.
These instances suggest the wealth of imaginary forms that can be obtained with simply suspended cables making an invisible form visible! In a later post I will talk about how nets and cables also make other invisible phenomena such as fluid dynamics (eg wind) or stress trajectories (eg highly sheared net sections) visible.
Now we focus on nets and networks. In nature, we are most familiar with an axisymmetrical spider net with cables originating from a center with a series of ring cables. The ring cable segments of the outer rings are always large that the inner ones, unless there are subdivisions. As a side note, these spider nets are mostly vertical single-layer surfaces, intended to catch prey. A lot of research has been done on orb radial nets: their radial “cables” are much stiffer than their ring “cables” to optimally absorb the energy of the prey impact. The stiffer radial cables also make sure that the spider can travel around in the web.
The artist Toshiko Horiuchi MacAdam handmakes crocheted radial net segmented which are then assembled in the most amazing colorful playscapes. The crochet technique alleviates the need for a knotted connection and as a result has a lot more stretch to it.
The radial arrangements lends itself to planar (think spiderweb) and curved forms (including synclastic, anticlastic and cone-like shapes) by draping, prestressing or adding rings to them.
A draped radial net picked up at a central point and suspended from an inclined large compression ring forms the basis of shape of Janet Echelman’s sculpture “She Changes” at Porto.
But nets do not need to be radial. In nature there are plenty of non radial nets and meshes. I juxtaposition here the natural rectangular net of the Hydropsyche with a square mesh with a rather similar looking hammock system.
Going from surface to volume defining, nets in nature sometimes fill or enclose a volume. The artist Thomas Saraceno emulates these volume filling nets in some of his works while Ernesto Neto encloses volumes with his nets and fabrics.
The detailing of the support conditions Neto’s works is exquisite: his tensile volumes are not permanently anchored to the site. His supports are carefully shaped volumes, weighed down with turmeric, clove and sand, no tensile anchors.
The Dipluridae spider does not create a 3D volume but a 2D net tunnel. I can but wonder whether Numen found part of their inspiration when they envisaged their Odeon Tape/Vienna piece. More than 270 rolls of adhesive tape measuring 14480 meters and weighing 30 kilograms, were shaped through a choreographic sequence in a climbable network.
For this artwork, the existing rigid columns supported the structure. However in natural nets, we see that the boundary conditions often are flexible, like blades of grass that can accommodate through bending-active action accommodate the large displacements of the nets. We see this also in bending active designed forms prestressed by nets or membranes. the relative flexibility of the boundary splines allow the tensile network to deform.
When spider nets are attached to rigid boundaries (like a stone for example), we see that the spider makes many connection links. The idea is that when the net moves and the boundary does not, some of the links go slack but due to he redundancy in the connections links there are always some that will be tensioned and maintain a structural capacity. Again we also see in the Numen Tube for Innsbruck, a tubular system of nets attached through tensile links to rigid surfaces a very large number of connections which ensures redundancy in the support system and hence guaranteed support.
A last and rather unusual flexible manner to support a net is through a pressurized flexible bubble like the water spider does to hover the net above its eggs.
The similarities between different components of natural nets and artistic net installations are striking: they make visible the invisible, allow for large deformations and yet are safe. At the Onouye architectural studio at the University of Washington, we continue our journey as we deepen our understanding of how nets and humans interact to make the invisible visible. Stay tuned for more posts.