I would much rather make a bow from billets that grew side by side in a stave. With a full length stave you often have wider rings on the bottom and more narrow ones on the top, clear wood on the bottom and more pins as you go up.
With sister billets you get closely matched wood in each piece.
Takedowns are a pain to build and not for the beginner, spliced billets are the way to go.
Draw out your pattern on a piece of paper;
Draw a centerline on your billet and glue the pattern onto the stave with white Elmer's glue and orientate the pattern in line with the centerline.
Cut out your pattern on the wood, the picture is of a limb replacement;
Sometimes the fit won't be very good, a little sanding and filing the high spots to fit may be necessary before glue up.
Done deal;