On shallow ellipses, the method of using two foci and a loop of string does not work. The stretch of the string will lead to inaccurate results. Even dacron, steel, graphite, and others have too much stretch.

Recently, I faced the task of creating an elliptical dome in an elliptical shaped coffer. The opening for the coffer was 9.5 feet on the short axis and 19 feet on the long axis. The elliptical dome inside this coffer was only 11 inches high. We couldn’t get any kind of line to work with traditional methods. Here is what we did.

First I drew the ellipse in autocad. I wanted 64 ribs for the shape so I used autocad to segment the elliptical line into 128 segments. I deleted every other one including the minor and major axis. This gave me four identical sets of 16 ribs. I simply needed 16 patterns. I used autocad to derive the length of each of these sixteen segments from the segment point on the edge to the center point.

Once I had the lengths of the ribs, I used autocad to create an ellipse with a minor axis of 11″ and a major axis of each of the the rib lengths. After I had created the 16 ellipses, I quartered them. I now had the shape of my 16 ribs. I added a horizontal and vertical axis line. On the horizontal axis line, I added six inches in width to each shape so that it would not come to a long sharp point. More on that later. I then nested them together inside a rectangle that was six feet wide and 48 feet long.

This is where the fun part starts. I took the electronic file to a sail shop that makes sails for sailboats. They had a computer controlled cutting table. They rolled out a sheet of reinforced mylar on the table and fed in the electronic file that I supplied them. The machine then cut out our sixteen patterns. I took these back to the job.

We used 1 1/8″ plywood for the ribs. We layed the patterns out, subtracting back out the six inches that we added for strength. Then we just spray painted a stencil of the pattern onto the plywood. We made four of each pattern and then fastened them into place.

For the center, I determined that I could use an ellipse of a certain size that I figured out mathmatically. I cut this out of 3/4 plywood and the size of it allowed me to zip off each rib to butt into it. The cut ends were 1″ thick and the shape just flowed into the 1/4″ difference in thicknessbetween that and the 3/4″ plywood center. The finish will be done in plaster of course. The 3/4″ center ellipse section was about 34″ long and 17″ wide and I had the computer cutting machine cut it out and lay out the segments in pen from a layout that I included in the electronic file. The machine can use either a cutter or a pen.

The autocad work took me 45 minutes. The cutting machine took another 45 minutes. Making and installing the ribs to two men two days. The frame was too pretty to cover. I thoroughly enjoyed developing the method and executing it and when we were done we just through the patterns in the dumpster. I really doubt that I will be asked to do this again and if I did the dimensions would be different.

Traditional methods are fine but developing new methods that work better are at least as fulfilling.