Several years back I made a 48" flat bow from black locust and backed with rawhide. If I remember it draws around 24". I did several things wrong but seem to have gotten away with it. However its is only a wall-hanger. The string I made from artifical sinew and the bow had a tremendous degree of natural recurve, so whenever I tried to string it the bow returned to natural shape--very strong. I refused to use dacron, I was afraid to take off any more wood, so it is a decorated wall-hanger .
If your stave is smaller it probaly has a pretty round back, so that will be a factor to work with. Also be sure you take off all the sapwood or down to the last ring or two. I know this advice isn't much. Good luck, BL is a strong, springy wood when tillered right.