Geometric mean radius of conductor bundle

The formula for round conductors was taken from the book 'Electric Power Generation, Transmission, and Distribution' by Leonard L. Grigsby (2006), chapter 14.1.2.3.

The formula for shaped conductors was taken from the paper 'Series impedance of distribution cables with sector-shaped conductors' by Andrew J. Urquhart (2015)

Symbol
$GMR_{bundle}$
Unit
mm
Formulae
$\left(GMR_c {s_c}^{n_c}\right)^{\frac{1}{n_c}}$two and three round conductors with same separation
$4^{\frac{1}{16}} \left(GMR_c {s_c}^3\right)^{\frac{1}{4}}$four round conductors with same separation