Geometric constant of circle with characteristic diameter

The geometric constant of the circle with the characteristic diameter $D_{x}$ is based on the book 'Kabel und Leitungen für Starkstrom' by L. Heinhold, 5th edition 1999 (in German).

Symbol
$g_{x}$
Unit
p.u.
Formulae
$\sqrt{-1 + \frac{4 L_{c}^{2}}{D_{x}^{2}}} + \frac{2 L_{c}}{D_{x}}$Daily load cycle
$\sqrt{-1 + \frac{4 L_{c}^{2}}{D_{x_{w}}^{2}}} + \frac{2 L_{c}}{D_{x_{w}}}$Weekly load cycle
$\sqrt{-1 + \frac{4 L_{c}^{2}}{D_{x_{y}}^{2}}} + \frac{2 L_{c}}{D_{x_{y}}}$Yearly load cycle
Related
$D_{x}$