Loss factor of steel pipes for pipe-type cables

The loss in steel pipes of pipe-type cables is given in the IEC by two empirical formulae, one for cables where the cores are bound in close trefoil formation and the other where the cores are placed in a more open configuration (cradled) on the bottom of the pipe. We calculate the ratio of the pipe inside diameter to cable outside diameter and if this ratio is larger than 3, cradled configuration is assumed otherwise triangular.

To be noted:

Symbol
$\lambda_3$
Formulae
${10}^{-5}\frac{0.0115s_c-0.001485Di_{sp}}{R_c}\left(\frac{f}{60}\right)^2\sqrt{\frac{60}{f}}$three single-core cables in trefoil in magnetic steel pipe
${10}^{-5}\frac{0.00438s_c+0.00226Di_{sp}}{R_c}\left(\frac{f}{60}\right)^2\sqrt{\frac{60}{f}}$three single-core cables in cradled formation in magnetic steel pipe
$\lambda_S \frac{1}{\left(\frac{R_{sp}}{R_{sp,S}}\right)^2 \sqrt{\frac{R_{sp,S}}{R_{sp}}}}$other pipe material than steel
$0$pipe-type cables with flat-wire armour over all three cores after they are laid up