# Geometric factor $G_1$

The calculation of thermal resistances of the internal components of cables for single-core cables is straightforward. However, the calculations of two- and three-core cables are more complicated and rigorous mathematical formulas cannot be determined, but mathematical expressions to fit the conditions have been derived. The general method employs geometric factor in place of the logarithmic term for single-core cables according to IEC 60287-2-1.

The quantity $G_1$ for two- and three-core cables with round conductors is given graphically in IEC 60287-2-1, Figure 2 and 3.

Symbol
$G_1$
Formulae
 $\ln\left(\frac{1-\alpha_M \beta_M+\sqrt{\left(1-{\alpha_M}^2\right) \left(1-{\beta_M}^2\right)}}{\alpha_M-\beta_M}\right) M_s$ Multi-core cables with round conductors $\ln\left(1+\frac{2t_1}{d_c}\right)$ Three-core cables with separate sheaths $2\left(1+\frac{2.2t_{2i}}{2\pi \left(d_x+t_{2i}\right)-t_{2i}}\right) \ln\left(\frac{D_f}{d_c}\right)$ Two-core cables with sector-shaped conductors $3\left(1+\frac{3t_{2i}}{2\pi \left(d_x+t_{2i}\right)-t_{2i}}\right) \ln\left(\frac{D_f}{d_c}\right)$ Three-core cables with sector-shaped conductors, belted $3\left(1+\frac{3t_{2i}}{2\pi \left(d_x+t_{2i}\right)-t_{2i}}\right) \ln\left(\frac{D_f-2t_f}{d_c}\right)$ Three-core cables with sector-shaped conductors, screened
Related
$d_c$
$D_f$
$d_x$
$t_1$
$t_{2i}$
$t_f$
Used in
$T_1$
Image
IEC standard 60287-2-1 Ed. 2.0 (2015) Figure 2 (left) and Figure 3 (right)