This is a modified batwing sail. These sails have a long heritage in canoe sailing, and are also seen in commercial kayak sail rigs. 

This rig has one batten in the top part of the sail.  The tension on the batten is adjustable to allow for changing the sail shape to match the wind speeds and whether you are going up or down wind.

Two reef points are built into the sail, to allow the sail area to be decreased from the 25.2 square feet of sail area fully deployed. 

The sail was made from a pvc coated camping tarp, metal grommets, and a sailboat sail batten, with a piece of aluminum 1 inch dia tube for a boom.  Later, I made a laminated wood boom for the sail that incorporated a sleeve that the mast fit through. 

In the top photo you can see an earlier version of aka and amas I was using.  The aka was poplar, and the amas were stitch and glue marine ply, connected to the aka by wingnuts.  It worked well, but was more difficult to store, and has less volume than the folbot amas I am using now.  However, the stitch and glue amas had a much more aerodynamic shape, which allowed much faster sailing at low wind speeds.

The third photo shows, in addition to a really badly trimmed sail, the locations of the reef points and the sewn in darts in the sail shape.  The third photo is also the sail rig I used on my stitch and glue kayak.  This kayak, with significant rocker, was a very responsive sailer, but structurally was not really made to handle high wind sailing.

The fourth photo shows the same model of sail rig on the two different boats.  Both sails are shown with one reef taken in to reduce the sail area. 

I have posted the diagram for the sail construction layout and the dimensions for the sail in the next two graphics.  These are copyrighted, but I will allow their use for non-commercial purposes by people who will build and sail the rigs.

 I've sailed the rig on the yellow boat in winds up through small craft advisories.  Sailing upwind with a kayak loaded with camping gear through 2 foot waves in a small craft advisory is a wet ride!