An ellipse $E(a,b)$ is given at its initial position by equation:
$\frac{x^2}{a^2}+\frac{(y-b{)}^2}{b^2}=1$

The ellipse rolls without slipping along the $x$ axis for one complete turn. Interestingly, the length of the curve generated by a focus is independent from the size of the minor axis:
$F(a,b)=2\pi max(a,b)$

This is not true for the curve generated by the ellipse center. Let $C(a,b)$ be the length of the curve generated by the center of the ellipse as it rolls without slipping for one turn.

You are given $C(2,4)\approx 21.38816906$.

Find $C(1,4)+C(3,4)$. Give your answer rounded to $8$ digits behind the decimal point in the form ab.cdefghij.