well, amigo, if ur piece of red oak is a uniform thickness...
mark center, and measure 4 inches either way, make a square line across the piece of wood.
draw straight tapers from these lines to the tips, so that the tips are 1/2 inch wide...
that should do it: the bow will bend through the handle, so you have to leave the handle full width or risk it breaking...also, you won't be able to glue any handle thickeners on, because the constant flexing and relaxing will cause them to pop off...you just wrap the handle with leather or something...