It would make sense. The two retaining arms would be sufficient to ensure the wood doesn't flex or break in use. A nice wooden compass could be made quite attractively as well, with some nice decoration and so forth.

I might just look through my stock and find some nice straight grained wood for this project, some split stock I would think. Of course it would have to be hand tooled! It would just seem wrong to use power tools to make a Medieval compass...

What would be a good wood as far as stiffness and strength. It would need to be able to have holes in it and metal fasteners.

I will draw up some plans and see what I can come up with!