Here's a simple plank thicknessing fixture (for a Hand Power Planer (like the 3" Makita planer.) The fixture holds the planer in place (to keep it from running away), and a couple side rails (spacers) slightly thicker than the desired result hold the planer off the bed. Just feed stock through until the planer settles onto the rails and stops cutting. Build this in 15 minutes, and get back to work on the models!

Using a hand plane, plane a thin shaving off the edge of a board. Cover a dowel with plastic wrap. Spread glue on the shaving and wrap it tightly around the dowel to produce a laminated tube. When dry, clean up the resulting tube and cut hoops off with a razor saw, or chuck the dowel in a drill or lathe and use a knife, saw, or parting tool to cut rings free.

Fine grained hardwoods work better than softwood - the shavings seem to stay together better and the resulting hoop is stronger. A fine grain structure that still shows in the finished hoop is good to simulate the oak of a full sized hoop. Use a wood with smooth grain that planes easily. Poplar works well. Dampen the shaving and iron it flat to take out any ripples and waves in the grain. 

Since it's hard to get a completely tight winding, I use a slightly tapered dowel covered in plastic wrap, and wrap a glue-covered strip as tightly as I can around the dowel at a point slightly smaller than my intended result.  Secure this with a couple wraps of masking tape, then force it towards the thicker end of the dowel while twisting it as if trying to "unwind" it. This clamps the layers together, binding them between dowel and masking tape to give nice tight laminations.  I use yellow carpenters glue (TiteBond). You may want to dampen the strip or thin the glue slightly before use. Expect to get glue all over your fingers.