Geometric constant of circle with dried-out soil

The geometric constant of the circle where the soil has dried out $D_{dry}$ is based on the book 'Kabel und Leitungen für Starkstrom' by L. Heinhold, 5th edition 1999 (in German).

Symbol
$g_{dry}$
Unit
p.u.
Formulae
$e^{\frac{2\pi \Delta \theta_x}{\rho_4 n_c \left(\mu W_I+W_d\right)}}$single cable, $D_{dry} > D_{x}$
$e^{\frac{\frac{2\pi \Delta \theta_x}{\rho_4 n_c}+\left(1-\mu\right) W_I \ln\left(g_x\right)}{W_I+W_d}}$single cable, $D_{dry} < D_{x}$
$e^{\frac{2\pi \Delta \theta_x}{\rho_4 N_c \left(\mu W_I+W_d\right)}}$two/three cables touching, $D_{dry} > D_{x}$
$e^{\frac{\frac{2\pi \Delta \theta_x}{\rho_4 N_c}+\left(1-\mu\right) W_I \ln\left(g_x\right)}{W_I+W_d}}$two/three cables touching, $D_{dry} < D_{x}$
$e^{\frac{2\pi \Delta \theta_x}{\rho_4 N_c \left(\mu W_I+W_d\right)}}$two/three cables flat with spacing, $D_{dry} > D_{x} > 2s_{c}$
$e^{\frac{\frac{2\pi \Delta \theta_x}{\rho_4 N_c}+\left(1-\mu\right) W_I \ln\left(g_x\right)}{W_I+W_d}}$two/three cables flat with spacing, $D_{x} > D_{dry} > 2s_{c}$
$e^{\frac{\frac{2\pi \Delta \theta_x}{\rho_4}+2\left(\mu W_I+W_d\right) \ln\left(g_a\right)}{\mu W_I+W_d}}$two/three cables flat with spacing, $2s_{c} > D_{dry} > D_{x}$
$e^{\frac{\frac{2\pi \Delta \theta_x}{\rho_4}+N_c \left(1-\mu\right) W_I \ln\left(g_x\right)-2\left(W_I+W_d\right) \ln\left(g_a\right)}{W_I+W_d}}$two/three cables flat with spacing, $D_{x} > 2s_{c} > D_{dry}$
$e^{\frac{\frac{2\pi \Delta \theta_x}{\rho_4}+\left(1-\mu\right) W_I \ln\left(g_x\right)-2\left(\mu W_I+W_d\right) \ln\left(g_a\right)}{W_I+W_d}}$two/three cables flat with spacing, $2s_{c} > D_{x} > D_{dry}$