John D
Difficult one. There are lots of images on the net of bows, but the good ones are mainly from manufacturers and are generally (a) taken at an angle, so don't give a good profile and (b) taken with the bow undrawn. Part of the challenge is that the limbs on a recurve vary in thickness and width, so the shape change as the bow is drawn is not straight-forward. I suspect even the manufacturers do not define the shape of limbs mathematically, so you're probably looking at a drawing not an equation. I've listed some web pages below which try to address the physics of recurve bows, and a couple of manufacturers who might provide suitable images for you to try.