I was wondering if there were any longbows in history with a relatively flat belly?
High draw weight warbows with a belly that is not that rounded?
Elm longbows with a flatter belly than ususual?
First quick thoughts. There is one bow from the Mary Rose (X1-3 IIRC) that is, I think, the only one not of yew (elm probably), which has a noticeably flatter belly.
(I think there's an article on this one on the Welsh Warbow website).
Also I believe some of the heavier yew Mary Rose bows have a squarish 'slab-sided' section, hence a fairly flat belly.
It is a basic principle that where the wood is more stressed (less resistant wood, or very high weight) it is necessary to spread the compression force, via flatter belly, more length etc.
So when I got a cheapish stave recently, with rock maple for the belly - I tried all these - a flattened oval cross-section (so about half the width of the belly is flat), length (6' 4" for 29" draw) and D-tillered to spread the compression over the whole length. It's still taken more set than I'd like, but less than I expected (no more than many lemonwood bellies I've seen).
Also I believe some of the Eastern Woodland Indians in the US made rectangular-section longbows?