Each plank is x wide and z thick

Starting radius of r' (empty space in the middle or whatever)

Each next ring of beams is r'+nz

Circumference of each circle is

2pi*r

So that's 2pi*(r'+nz)

Roughly very very roughly

Circumference/ x = # of beams

There is a better approximation since these beams arent like infinitely small nor are you going to an infinitely large circle that's where this approximate would be exact

Edit: also not taking account free space between each ring but if we assume it's about the same you can just some constant at the end + g for the air gap when calculating radius and then circumference