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:

• The loss-factor is per phase.
• The IEC notes that these formulae have been empirically obtained in the United States of America and at present apply only to steel pipe sizes and steel types used in that country.
• The formulae given apply to a frequency of 60 Hz. For lower frequencies, the induced current in the ferromagnetic steel pipe will be lower and for higher frequencies it will be higher. So for other frequencies, each formula is multiplied by a correction factor. For 50 Hz, the factor is 0.76 and for 16.7 Hz it is 0.147.
• Symbol
$\lambda_3$
Formulae
 ${10}^{-5}\frac{0.0115s_c-0.001485Di_{sp}}{R_c}$ three single-core cables in trefoil in magnetic steel pipe ${10}^{-5}\frac{0.00438s_c+0.00226Di_{sp}}{R_c}$ three single-core cables in cradled formation in magnetic steel pipe $\lambda_3 \left(\frac{f}{60}\right)^2 \sqrt{\frac{60}{f}}$ other frequencies than 60 Hz $0$ pipe-type cables with flat-wire armour over all three cores after they are laid up
Related
Used in
$I_c$
$T_{eq}$
$T_{int}$
$\theta_{c,z}$
$W_h$
$W_I$
$W_{sp}$