I decided to base my design for this dome on a catenary curve because it is the optimum shape for a self supporting arch.
The Gateway Arch is an example of a self supporting arch based on a catenary curve.
The equation for the catenry curve I chose is f(x)=(4*cosh(2.5))-(4*cosh(x/4)).
This is in units of feet. Over the range 0 to 10 it looks like: