How can I calculate a specific diameter hole (28.5 mm) for a hyperboloid center opening when it's Z=0

Question

How can I calculate a specific diameter hole (28.5 mm) for a hyperboloid center opening when it's Z=0

The arrows point to where z=0 and the 28.5mm hole should be.

I'm using python

The snippet of python code / formula I'm using is below:

        u = 8*(i/num_x-1/2)
        v = 2*math.pi*(j/(num_y-1)-1/2)

        x = uval_a*math.sqrt(1+u*u)*math.cos(v)
        y = uval_a*math.sqrt(1+u*u)*math.sin(v)
        z = uval_b*(u)
            
          

Answer 1

Those constants -- uval_a and uval_b -- serve exactly that purpose.

uval_a is the radius of the center circle, so you shoudl set

uval_a = 28.5 / 0.5

assuming that you're working in mm units everywhere. What about uval_b? That tells you how tall the hyperboloid is.