Perhaps I invented a new mathematical shape; if you've seen this elsewhere in the literature please let me know.

It is a spinning rope sculpture based on the interplay between centrifugal effects, gravitational effects, and tension in the rope.

As an art installation it is a kinetic sculpture with a characteristic "teardrop" shape in the fundamental mode, going to other shapes in higher modes.

Using RGB (Red Green Blue) addressable LED rope, I've created a kinetic light sculpture that maps sound waves and other phenomena.

Supplies

A rope dangles onto a turntable. The turntable spins causing the rope to fling out due to centrifugal effects, while gravity acts on the rope at the same time. Here the rope is about 12 feet long on a 10.5 foot rise from the turntable up to the pivot point.

Step 1: Dangle a Rope Onto a Turntable

Here the rope is 10 metres long and the rise from turntable to the top is 25 feet. A hollow structural steel beam cantilevers out about 8 feet in front of the building, and a turntable is also out about 8 feet from the front of the building.

The rope is lit, 36 pixels per metre, weighting about 95 grams per metre.

Photographs are shown leftmost extreme motion in fundamental mode, and rightmost, as well as double-exposure showing the Mochord shape.

Mochord as in Motor (abbreviated to 2 letters as in words like "Motel" = Motor Hotel, and the word "motor" itself deriving from "movere", i.e. motion), and "chord" meaning "string" in Greek (in this case a string of lights).

Step 2: Have Some Fun With the Math

Solve the math and win a prize.

There's a contest for best solution.

See mersivity.com/prizes.htm

Step 3: Spin It Up

Once spinning, it creates a magical sense of awe and wonder as a Mochoid, "oid" as in "ellipsoid" or "catenoid".

Step 4: Compound Motion

Once you have it spinning, consider mounting it to a moving rollcart or wagon, and while it is spinning, also push it along. With light rope you'll get a wonderfully magical long-exposure photograph like the ones shown above, especially if you can get it to "mode hope" where it jumps from the fundamental shape to a higher state.