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External diameter conductor, transient

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
$d_{c,t}$
Unit
mm
Formulas
$d_{c}$single-core cables
$\sqrt{2} d_{c}$two-core cables, round conductors
$D_{i,t} e^{\frac{-2\pi T_{1}}{n_{c} \rho_{i}}}$three-core cables, round conductors
$d_{x}$multi-core cables, sector-shaped conductors
Related
$d_{c}$
External diameter conductor [mm]
$D_{i,t}$
Diameter over insulation, transient [mm]
$d_{x}$
Equivalent diameter conductor [mm]
$n_{c}$
Number of conductors cable
$\pi$
Archimedes' constant $\pi$
$\rho_{i}$
Thermal resistivity insulation material [K.m/W]
$T_{1}$
Thermal resistance conductor—sheath [K.m/W]
Used in
$A_{i,t}$
Cross-sectional area insulation (IEC 60853) [mm$^2$]
$p_{i}$
Apportioning factor insulation
$Q_{i,t1}$
Thermal capacitance insulation, 1st portion (IEC 60853) [J/(m.K)]
$Q_{i,t2}$
Thermal capacitance insulation, 2nd portion (IEC 60853) [J/(m.K)]
$t_{1,t}$
Thickness conductor—sheath, transient [mm]