The characterisitc diameter $D_x$ is the location at which the effect of the loss factor commences.

The calculation of the characteristic (or fictitious) diameter for sinusoidal load is based on the IEEE paper 'Ampacity calculation for deeply installed cable' by E. Dorison, dated 2010. The calculation uses the modified Bessel function K of order 0: k0() and the modified Bessel function of the first kind of order 1: k1().

The IEC standard 60853 uses an approximation with an exponential integral valid for an infinite thin wire whereas the formulas presented in the paper the cable diameter influences the diameter of the area affected by load variations. This is particularily important for cables in tunnels, where the tunnel diameter replaces the diameter of the cable.

Based on the evaluations by Neher, the characteristic diameter becomes 212 mm. For more details, refer to $K_x$.

$D_{\mathrm{x}}$

mm

$1020 \sqrt{\delta _{\mathrm{soil}} \tau}$ | Method by Neher McGrath |

$D_{\mathrm{e}} e^{\frac{2000}{D_{\mathrm{e}} q_{\mathrm{x}}} \operatorname{abs}{\left (\frac{\operatorname{k_{0}}{\left (\frac{D_{\mathrm{e}} q_{\mathrm{x}}}{2000} \right )}}{\operatorname{k_{1}}{\left (\frac{D_{\mathrm{e}} q_{\mathrm{x}}}{2000} \right )}} \right )}}$ | Method by Dorison |

$\delta _{\mathrm{soil}}$

Soil thermal diffusivity [m²/s]

$q_{\mathrm{x}}$

$\tau$

Transient period [s]

$T_{\mathrm{4d}}$

$T_{\mathrm{4et}}$

Transient thermal resistance [K.m/W]