/diy/ - Do It Yourself

Hey /diy/, I tried asking /sci/ this (because math), but got no takers.

I'm trying to build a shelf for shot glasses.
I'd like it to be curved so the center is a little further from the wall than the ends.
I'd like it to be a certain width (about 30-32").
I don't want it to stick too far out from the wall (6-8").
and I'd like a smaller, second row of glasses behind the first row.
I know the math for finding the length of an arc of a circle, and a little trig also helps, but I keep coming back to trial and error for finding the right parameters for laying this out.
I've never taken calculus, and maybe that's the short answer, but how do I find the right combination of degrees of arc and radius to find a layout for x number of glasses spaced y distance apart without resorting to trial and error?