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.

$d_{c}$single-core cables and multi-core cables with sector-shaped conductors
$D_{ins} e^{- \frac{2 T_{1} \pi}{n_{c} \rho_{i}}}$three-core cables with round conductors
$\sqrt{2} d_{c}$two-core cables with round conductors