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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.

Formula for shaped conductors can be found in the paper 'Series impedance of distribution cables with sector-shaped conductors' by Andrew J. Urquhart (2015)

Symbol
$GMR_{cc}$
Unit
mm
Formulae
$\left(GMR_c \left(\frac{s_c}{1000}\right)^{n_c}\right)^{\frac{1}{n_c}}$two and three round conductors with same separation
$4^{\frac{1}{16}} \left(GMR_c \left(\frac{s_c}{1000}\right)^3\right)^{\frac{1}{4}}$four round conductors with same separation
Related
$GMR_c$
Geometric mean radius of conductor [m]
$n_c$
Number of conductors in object
$s_c$
Separation of conductors in a system [mm]
Used in
$GMD$
Geometric mean distance between phases of the same system [m]