# Loss factor of armour

The formulae express the power loss occurring in metallic armour and reinforcement of a cable in terms of an increment $\lambda_2$ of the power loss in all conductors.

The IEC standard has formulae for three distinctive cases: Non-magnetic armour or reinforcement, magnetic armour or reinforcement, and losses in steel pipes. we consider the losses in steel pipes of pipe type cables separately using $\lambda_3$ and allow for losses in ferromagnetic ducts using $\lambda_4$.

With non-magnetic armour or reinforcement, the general procedure is to combine the calculation of the loss in the reinforcement with that of the shield. The formulae are given in IEC 60287-1-1, chapter 2.3 and the parallel combination of shield and armour resistance is used in place of the single shield resistance $R_s$. The root mean square value of the shield and armour diameter replaces the mean shield diameter as shown in chapter 2.3.11. This procedure applies to both single, twin and multicore cables.

In case of single-core cables with magnetic armour or reinforcement with solid bonding, the loss factor $\lambda_2$ is calculated using the total loss in shield (screen$||$sheath) and magnetic armour as described in IEC 60287-1-1 chapter 2.4.2.1. In this case, the loss factors $\lambda_1$ and $\lambda_2$ may be assumed to be appoximately equal.

SL-type cables are typically three-core cables with separate lead sheaths. There is no definition given in the IEC 60287. We also consider three-core cables with separate copper and aluminium sheaths, flat or corrugated, with or without a jacket over the sheath, to be SL-type.

To be noted:

• When there is no armour present, then $\lambda_2$ = 0.
• The equation for steel tape armour is only valid for steel tapes between 0.3 and 1.0 mm thickness.
• For one-phase systems, armour loss factor is not calculated ($\lambda_2$ = 0).

Symbol
$\lambda_2$
Formulae
 $\frac{W_{sar}}{2W_c}$ single-core cables with magnetic armour and screen/sheath $\frac{W_{sar}}{W_c}$ single-core cables with magnetic armour and without screen/sheath $\frac{0.62{\omega}^2{\cdot}{10}^{-14}}{R_c R_{ar}}+\frac{3.82A_{ar} \omega{\cdot}{10}^{-5}}{R_c} \left(\frac{1.48r_c+t_{2i}}{{d_{ar}}^2+95.7A_{ar}}\right)^2$ two-core cables with steel wire armour $1.23\frac{R_{ar}}{R_c} \left(\frac{2c_c}{d_{ar}}\right)^2 \frac{1}{\left(\frac{2.77R_{ar}{\cdot}{10}^6}{\omega}\right)^2+1}$ three-core cables with steel wire armour, with round conductors $0.358\frac{R_{ar}}{R_c} \left(\frac{2r_1}{d_{ar}}\right)^2 \frac{1}{\left(\frac{2.77R_{ar}{\cdot}{10}^6}{\omega}\right)^2+1}$ three-core cables with steel wire armour, sector-shaped conductors $\lambda_{21}+\lambda_{22}$ three-core cables with steel tape armour or reinforcement $\left(1-\frac{R_c}{R_e} \lambda_{11}\right) \lambda_{21}$ three-core SL-type cable with steel wire armour
Used in
$I_c$
$T_{eq}$
$T_{int}$
$\theta_{c,z}$
$\theta_{sp}$
$W_{ar}$
$W_h$
$W_I$
$Z_{pos}$