NETS AND DANCE: What do you know about nets?

In 2015 I received a phone call from Khalid Addi, professor at the University of Reunion, one of the islands in the Indian Ocean. This french island in the Indian Ocean, attracts surfers from all over the world to test their “surf”. In 2011 the first shark attacks started, officials closed beaches and the island’s tourism-based economy largely suffered. In the wave break zones of the beaches of Noires and Boucan Canot, protective shark nets barriers were installed. We explored how different net topologies mechanically interacted with the breaking waves. We discovered that there are no engineering textbooks on the mechanics of nets and that we had to start at the basics by studying the effect of mesh topology on the net response when waves loaded them Unlike the installed orthogonal meshed nets, we found that bias or hexagon meshed nets had larger negative Poisson’s ratio and could therefor provide the needed elongations and thus reduced forces in the net ropes.

sharkbarrier.png
Shark Barrier Net in Reunion Island.

Today I am at the University of Washington, to kick off an architectural studio with Prof. Tyler Sprague, structural engineer, on tensioned and draped nets. This studio is the precursor to a series of explorations with the fiber artist Janet Echelman and the choreographer Rebecca Lazier investigating how nets can be designed, engineered and tailored for visual and choreographic expression.

Unlike other structural systems (such as beams/columns, frames, trusses, shells or membranes), engineering students, generally speaking, do not learn about nets. Yet nets are ubiquitous in our daily lives: nets to catch fish or insects, safety nets to catch acrobats or falling stones, sport nets in tennis rackets, climbing and bridge nets, cablenet roofs, and nets to contain air, earth or oranges.

oranges
Unstressed and stressed net due to enclosed solids

Nets can be 1, 2 or three dimensional and their form is a function of the forces applied. In the example of the net hammock, a 1D net, the form is curved under the distributed loading of the bodies, yet straight where no load is applied (between the 2 people), resulting in a segmented shape. Under its self-weight only, a 1D net takes on the shape of a catenary (from the Latin “catina” meaning chain) like the seaweed plantation net spanning between lath supports.

A 2D (thus planar) net can either be stiff or it can be flexible. The tensioned tennis racket network exemplifies a stiff planar network. The prestressing in the strings, tensions the net and makes it deform “relatively” little when hit by a ball.

racket
Pretensioned net in racket

In contrast, slack 2D guard nets, deform a lot when impacted by skiers or a sky divers without a parachute.

By attaching a net to 4 or more out-of-plane support points, a 3D net form arises. The shape of a flexible fishing net, for example, is not mechanically prestressed, yet it is totally in tension under self weight. Its shape depends upon the position of the support points, the elasticity and diameter of the net material as well as the mesh type and size.

fishing net
fishing net under self weight

A 3D net can be made stiff through pre-stressing (like the string network in the 2D tennis racket) and/or through a doubly curved form. This form can either be synclastic (i.e. positive Gaussian curvature) or negative (i.e. negative Gaussian curvature).

positive

 

climbing nets
Anticlastic climbing net (Numer Tube)

To achieve synclastic curvature in a net, the net needs to pre-stressed with for example hair or air.

Stiff anticlastic 3D net forms rely on specific boundary conditions like arches, 2 high and two low points (sometimes called the saddle), a central high point and radially positioned low points (a cone) or alternating high and low points resulting in a ridge and valley system. This latter system is the most difficult to achieve anticlastic Gaussian curvature in. The cablenet roofs of the Munich Olympic Stadium clearly show anticlastic curved geometries in addition to the net being prestressed. As a result this 3D net roof is relatively stiff (but not as stiff as rigid roofs). Another rather stiff but not prestressed example of a net is the anticlastic catfish net.

munich
Munich Olympic Stadium – anticlastic cable net
catfish
Anticlastic Catfish net

In the architectural studio at the University of Washington, students explore how the nets can be designed to accentuate their dynamic expression under applied loading. This net exploration began with the physical form finding experiments of stiff 3D nets. This is the first task in the design and installation of a full scale artifact that will merge the disciplines of structural engineering, visual art and choreography.

model1
model architectural studio at the University of Washington
model2
model architectural studio at the University of Washington
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