50' is not a very big span for a bowstring & most timber design guides walk you through this; the Canadian Wood Council's design manual does a good job & I'd guess the American one is the same. A 1956 American wood design manual that I have also does it, & it's not too complicated for a simple bowstring tied arch (which you seem to describe, as opposed to a bowstring truss). However, I'm pretty well baffled by your description. The span is 50', the arch is an 11 3/4" X 7 1/2" glulam, which sounds reasonable, but the spacing is 2'? And the tie is a 2X6? This has to be unique in bowstring construction. I've built 60' span arched structures with glulam ribs, at 16" & 24" spacings, but they were 1 3/4" X 7 1/2" ribs (2x8s), not 8X12s.