External diameter of conductor for transient calculations

For calculation of the cyclic and emergency current rating of cables acc. IEC 60853, the multi-core cable is replaced by an equivalent single-core construction dissipating the same total conductor losses. The equivalent single-core conductor has a diameter as calculated by the formula below where $D_i$ is the value of diameter over insulation and $T_1$ the thermal resistance for the multi-core cable.

The actual conductors are considered to be completely inside the diameter of the equivalent single-core conductor, the remainder of the equivalent conductor being occupied by insulation.

Symbol
$d_{ct}$
Unit
mm
Formulae
$d_c$Single-core cables
$D_{it} e^{\frac{-2\pi T_1}{n_c \rho_i}}$Three-core cables with round conductors
$\sqrt{2} d_c$Two-core cables with round conductors
$d_x$Multi-core cables with sector-shaped conductors