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Geometrical distance factor for multi-core cables

The factor for two-core cables with round conductors is equal to 2.
The factor for three-core cables with round conductors is equal to $2.1547=1+2/\sqrt 3=1/(2 \sqrt 3 -3)$.

Symbol
$F_x$
Formulae
$1$Single-core cables, round conductors & Multi-core cables, sector-shaped conductors
$1+\frac{1}{sin\left(\frac{\pi}{2}\right)}$Two-core cables, round conductors
$1+\frac{1}{sin\left(\frac{\pi}{3}\right)}$Three-core cables, round conductors
$1+\frac{1}{sin\left(\frac{\pi}{4}\right)}$Four-core cables, round conductors
$1+\frac{1}{sin\left(\frac{\pi}{5}\right)}$Five-core cables, round conductors
Related
$F_{eq}$
Factor for envelope circle for a group of equal circles
$\pi$
Archimedes' constant $\pi$
Used in
$D_{ab}$
Diameter over armour bedding [mm]
$D_{core}$
Diameter over core cable [mm]
$D_{eq}$
Equivalent diameter of a group of round objects [mm]
$D_f$
External diameter of the filler [mm]
$D_{is}$
Diameter over insulation screen [mm]
$D_{it}$
Diameter over insulation for transient calculations [mm]
$d_s$
Equivalent diameter of screen and sheath [mm]
$D_{scb}$
Diameter over screen bedding [mm]
$D_{shb}$
Diameter below sheath [mm]
$s_c$
Separation of conductors in a system [mm]
$T_{ab}$
Thermal resistance of armour bedding [K.m/W]