The Cherokee built hunting bows and war bows. Both were bend through the handle bows. The hunting bows were like John described and the war bows, as described in TBB2 is 72 1/4" long,
1 9/16" at the handle and 1 1/16" at the tips and drew 60# to 80# and more.
These bows were typically black locust while the Cherrokee were living in the Southeastern US but once they were moved to Okalahoma they switched to osage. Either osage or persimmon would work for the bow you want to build.