Clouds

George W. Hart

I recently installed this large metal sculpture, Clouds, in the Simons Foundation building in New York City.  It consists of two mirror-image orbs, each five feet in diameter and two and a half feet tall.  Each orb is made from sixty flat aluminum components (in four different shapes) that fill an ellipsoidal volume.

It's hard to capture the effect of the sculpture in a still photograph.  Although they are metal, they feel like they float lightly in the air.  From some positions, one is struck by geometric details, such as their six five-sided tunnels, one of which is emphasized in the image above.  But from other positions, they give the impression of a 3D version of a scribbled drawing of an amorphous cloud.

My design process is centered on computer models, which I edit repeatedly until I'm happy with all aspects of the design.  I write my own custom software for this, as existing 3D design packages don't have the mathematical features I want.

For this design, the next step was to make a small-scale model from laser-cut plywood.  I led a group of students in this construction while visiting the Rochester Institute of Technology. You can see the parts are held together with small cable ties. Cable ties are great for this because they're strong, easy to connect, and adapt to any dihedral angle between the planes.

The next stage was to make a full-scale wood version of both mirror-image orbs, each five feet in diameter.  These are currently on display in the Wang Center at Stony Brook University.  You need to look carefully to observe that they make up a matched left-handed and right-handed pair.

These are also assembled with cable ties in a student workshop, in this case as part of a summer math program at Stony Brook University.  This allowed me to practice the assembly sequence and work out the best way to partition the structure into smaller modules.

Finally, I prepared the metal parts.  They are laser-cut from aircraft aluminum in the four different shapes shown above.  The four variations are related by affine transformations (stretching and compression in various directions) as a result of the way the overall form is derived.  I also had to engineer the 360 brackets that connect the pieces and work out the best locations for the bolt holes.

Before the day of the assembly, I attached one side of all the brackets and connected the support cabling to the upper pieces.  The brackets had been pre-bent to seven different angles in order to account for the various dihedral angles between the planes.   In addition to keeping track of which bracket goes where, one must also remember that the bracket attaches to one side or the other of a piece depending on whether it is for the left-handed or right-handed orb.

I invited some friends to help and we spent much of a day assembling everything.  The first step is to make three-part modules, joining everything with stainless steel nuts and bolts.  The nuts have nylon inserts so they'll never loosen, but that makes them extra troublesome to put on.  (They're sometimes called "aircraft nuts" because they were invented to solve the problem of keeping airplanes from falling apart from vibration.)

We make twenty of the three-part modules, as there are sixty pieces for each orb.  We also need to keep track of the fact that there are two types (affinely related) of module.  The ones near the North and South poles are different from the ones near the equator.

The sculpture begins to take form as we connect the modules together.  It is a wonderful feeling to experience how everything fits together perfectly.  One advantage of laser-cutting is that it is accurate to better than a hundredth of an inch.

For the later stages, we can work on the floor, approaching it from all around as we continue to add modules.  Checking for loose nuts and getting everything tight takes a while, because all together there are 720 nuts, 720 bolts, and 1440 washers to take care of.

Finally the two orbs are complete!  Hanging them was then relatively quick, as eye-bolts had been installed in the ceiling ahead of time.  Here's a view from the floor, looking straight up, emphasizing the five-fold rotational symmetry of the design.  I'm quite proud of the way Clouds came out.