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
$e^{\frac{2 \Delta \theta_{x} \pi}{n_{c} \rho_{4} \left(W_{I} \mu + W_{d}\right)}}$single cable, $D_{dry} > D_{x}$
$e^{\frac{\frac{2 \Delta \theta_{x} \pi}{n_{c} \rho_{4}} + W_{I} \left(1 - \mu\right) \ln{\left(g_{x} \right)}}{W_{I} + W_{d}}}$single cable, $D_{dry} < D_{x}$
$e^{\frac{2 \Delta \theta_{x} \pi}{N_{c} \rho_{4} \left(W_{I} \mu + W_{d}\right)}}$two/three cables touching, $D_{dry} > D_{x}$
$e^{\frac{\frac{2 \Delta \theta_{x} \pi}{N_{c} \rho_{4}} + W_{I} \left(1 - \mu\right) \ln{\left(g_{x} \right)}}{W_{I} + W_{d}}}$two/three cables touching, $D_{dry} < D_{x}$
$e^{\frac{2 \Delta \theta_{x} \pi}{N_{c} \rho_{4} \left(W_{I} \mu + W_{d}\right)}}$two/three cables flat with spacing, $D_{dry} > D_{x} > 2s_{c}$
$e^{\frac{\frac{2 \Delta \theta_{x} \pi}{N_{c} \rho_{4}} + W_{I} \left(1 - \mu\right) \ln{\left(g_{x} \right)}}{W_{I} + W_{d}}}$two/three cables flat with spacing, $D_{x} > D_{dry} > 2s_{c}$
$e^{\frac{\frac{2 \Delta \theta_{x} \pi}{\rho_{4}} + \left(2 W_{I} \mu + 2 W_{d}\right) \ln{\left(g_{a} \right)}}{W_{I} \mu + W_{d}}}$two/three cables flat with spacing, $2s_{c} > D_{dry} > D_{x}$
$e^{\frac{\frac{2 \Delta \theta_{x} \pi}{\rho_{4}} + N_{c} W_{I} \left(1 - \mu\right) \ln{\left(g_{x} \right)} - \left(2 W_{I} + 2 W_{d}\right) \ln{\left(g_{a} \right)}}{W_{I} + W_{d}}}$two/three cables flat with spacing, $D_{x} > 2s_{c} > D_{dry}$
$e^{\frac{\frac{2 \Delta \theta_{x} \pi}{\rho_{4}} + W_{I} \left(1 - \mu\right) \ln{\left(g_{x} \right)} - \left(2 W_{I} \mu + 2 W_{d}\right) \ln{\left(g_{a} \right)}}{W_{I} + W_{d}}}$two/three cables flat with spacing, $2s_{c} > D_{x} > D_{dry}$
Related
$\Delta \theta_{x}$
$\mu$
$\rho_{4}$
$W_{d}$
Used in
$D_{dry}$