Self yew longbow

I have a strait yew log with virtually no knots and plan to make a Victorian style longbow. This is my second attempt. The first worked well but did not last. My problem with this one is that the piece is only 2 1/2 inches in diameter. So the sapwood back.is rounded. I think I will need to reduce this so it is close to flat. The grain runs strait down the piece so once planed it will show vertical stripes.

The question is will it be better to aim for a flat back or keep the rounded sapwood in tact?