Geometric factor $G_2$ for cables with separate sheaths

The geometric factor for three-core cables with separate sheaths is the digital calulation of the quantity G given graphically in IEC 60287-2-1, Figure 6, used to calculate the thermal resistance of filler material and armour bedding as part of $T_2$ for cables with separate sheaths.

Symbol
$G_{2}$
Formulae
$2 \pi \left(- 20.4762 X_{G2}^{2} + 2.11429 X_{G2} + 0.00022619\right)$sheaths touching, $0 < X_{G2} <= 0.03$
$2 \pi \left(10.6352 X_{G2}^{3} - 4.49737 X_{G2}^{2} + 1.17533 X_{G2} + 0.0142108\right)$sheaths touching, $0.03 < X_{G2} <= 0.15$
$2 \pi \left(- 21.6667 X_{G2}^{2} + 2.03214 X_{G2} + 0.00020238\right)$equal thickness between sheaths and between sheaths and armour, $0 < X_{G2} <= 0.03$
$2 \pi \left(11.5093 X_{G2}^{3} - 4.56104 X_{G2}^{2} + 1.101 X_{G2} + 0.0126529\right)$equal thickness between sheaths and between sheaths and armour, $0.03 < X_{G2} <= 0.15$
Image
IEC standard 60287-2-1 Ed. 2.0 (2015) Figure 5