Geometric mean distance between phases of the same system

The formula for the GMD was taken from the book Electric Power Generation, Transmission, and Distribution by Leonard L. Grigsby (2006), chapter 14.1.2.7.

Symbol
$GMD$
Unit
mm
Formulae
$a_m$conductor to conductor of single-core cables
$GMR_{bundle}$conductor to conductor in multi-core cables
$\left({a_m}^{n_{sw}}-\left(\frac{d_s}{2}\right)^{n_{sw}}\right)^{\frac{1}{n_{sw}}}$screen of single-core cable to conductor of other cable
$\left({a_m}^2-\left(\frac{d_s}{2}\right)^2\right)^{\frac{1}{2}}$sheath of single-core cable to conductor of other cable
$\left({a_m}^{n_{ar}}-\left(\frac{d_{ar}}{2}\right)^{n_{ar}}\right)^{\frac{1}{n_{ar}}}$armour of single-core cable to conductor of other cable
Used in
$X_0$