The rudder on my 20ft mahogony strip sailboat was 3/4" plywood rounded in
front and tapered in back. (taper to 1/8", or the thickness of the middle ply)
I broke the rudder cheeks running before a strong wind and had to replace
them, that's the two pices on either side at the top. It would not be
difficult to replace that sort of steering arrangement entirely. Maybe you can
replace your rudder cheeks with thicker ones made of plywood, and make a
plywood rudder as well. To do that measure the gap between the cheeks to
see how thick the plywood for the rudder has to be.

Good luck.


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