My butt may be big, but there's no song about your flat one.
-- Internet Meme
The Payson (Fiberglass) Butt
The Fiberglass Butt - shown in plan below the main illustration - has become a common means to join plywood sheet edge-to-edge, and works as well for patches.
Of it's provenance, Dave Carnell writes:
In 1986 I wrote about the joint in Small Boat Journal. About the same time "Dynamite" Payson wrote in Boatbuilder about a similar joint concept. Years later I discovered that Joe Dobler had used the principle well before our publication, as had Jack Chippendale in England.
This method includes variants in which the ply is step-layered to accommodate the fiberglass at or below surface level.
Payson produced this great illustration for a variant that's come to be known as the Payson Butt. He was kind enough to grant permission to reproduce it, back before the internet.
Recently I was shocked to be unable to find it posted entire (uncropped and showing the standard butt), so am putting it out now. This version has been lightly edited to clarify text that had been poorly digitized.
The Payson Butt was proposed (originally, so far as I'm able to determine) that the 'step' depression can be done as a ground-out dip, with the addition of the smoothing technique shown above.
According to Payson, the full method is unnecessary for strength (the plain fiberglass butt is sufficient), but smooths the hull for an aesthetically smooth finish.
Either way, it avoids simple-but-intrusive buttstraps and labor-intensive and sheet-shortening scarfs.
Dave Carnell uses multiple layers proportional to ply thickness. My understanding is that his schedule - 3 layers each side for 1/2in ply - is now considered conservative.
Consider weight of cloth, thread orientation (i.e., orthoganal , bi- or triaxial weaves) and adjacent structure for your particular application.
NOTE: A similar method can be used for wood repair... grind a fair, 12:1 curved dip (or as easy as space allows) across a break and lay in glued layers of wood, bent to the curve. Trim and finish. Works great for frames, but can also be used in place of graving or butt patches.