Well, I don't think the red and black would have to be full sized arcs(width-wise).
As long as you have the seam allowances (top/bottom) plus some wiggle room, that should be enough.
I mean, you don't have measure to the thread. ;-)
You should also have enough seam allowances on each side because you're really only cutting 1/2 the pieces for the arc (or as many as you can get out of one).
And I strongly suggest you try it with two scrap fabrics to make sure it would work.
It should also give you an idea of how large to cut the arcs for the red and black fabrics.
Theoretically, it should work.