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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
$\frac{2L_c}{D_x}+\sqrt{\left(\frac{2L_c}{D_x}\right)^2-1}$Daily load cycle
$\frac{2L_c}{D_{x,w}}+\sqrt{\left(\frac{2L_c}{D_{x,w}}\right)^2-1}$Weekly load cycle
$\frac{2L_c}{D_{x,y}}+\sqrt{\left(\frac{2L_c}{D_{x,y}}\right)^2-1}$Yearly load cycle
Related
$D_x$
Characteristic diameter [mm]
$D_{x,w}$
Characteristic diameter for weekly load [mm]
$D_{x,y}$
Characteristic diameter for yearly load [mm]
$L_c$
Depth of laying of sources [mm]
Used in
$g_{dry}$
Geometric constant of circle with dried-out soil [p.u.]