# Armour losses and double-layer armour

The IEC standard 60287-1-1 describes methods to calculate the armour loss factor but does so for one layer of armour only. Other ampacity calculation programs allow the user to model as well only one layer. This poses a certain problem to correctly calculate the losses of a cable with two armour layers such as submarine cables or certain three-core cables. In addition, Cableizer offers some further improvements in calculating armour losses as compared to its competitors or the IEC standard.

Posted 2015-11-20
Categories: New feature, Theory, User guides

The IEC standard 60287-1-1 describes methods to consider non-magnetic and magnetic armour or reinforcement and calculate the armour loss factor \$λ_2\$ with some simplifications.

• For non-magnetic armour, the general procedure is to combine the calculation of the armour losses with that of the sheath, meaning a parallel combination of sheath and armour resistance is used in place of the single sheath resistance \$R_s\$. This implicates that the bonding of screen/sheath and armour have to be identical.
• For magnetic armour, the method does not take into account the possible influence of the surrounding media. For single-core cables, the method is intended for installations where spacing between cables is large or where the influence of the surrounding media can be ignored, e.g. in air. Again, a parallel combination of sheath and armour resistance is used.

### Second armour layer

The method in the IEC standard only describes one layer of armour, for example round steel wires. To model cables with two armour layers, one can try to adjust the diameter of the armour wires to reach the same resistance as for the two layers combined. Not only is this a hassle, it results in a false diameter of the jacket and therefore in a false value of its thermal resistance \$T_3\$ as well as in a deviation in the thermal resistance \$T_4\$ of the environment. However, there is no limitation to double the layer and do the calculations separately for each layer.

With Cableizer you can now define two separate layers of armour of the same type but with independent input values for:

• diameter for round wires
• height and width for flat wires
• thickness for tape or TECK armour
• number of wires
• length of lay
All calculations are made separately for both layers. By doing so, a separate armour loss factor for each layer is calculated and at the end added together to get \$λ_2\$ used in the current rating calculations. These calculations are done for each iteration step. With this approach, the dimensions are identical to the real cable resulting in correctly calculated values of thermal resistance \$T_3\$ of the jacket and \$T_4\$ of the surrounding.

### Improvements over the IEC standard

The methods in the IEC standard to calculate the armour losses use several simplifications. Because Cableizer is not really limited in calculation power, some of these simplifications have been dropped.

• In Cableizer, the cross-sectional area of steel tape or TECK armour is calculated directly from the armour thickness \$d_f\$, assuming a filling ratio of 1.0. If that is not the case in practice, i.e. the armour thickness is larger than the thickness of a solid cylinder with the cross-sectional area of the armour, you should add some thickness to the armour bedding and outer sheath, in order to get the correct mean diameter of armour \$d_A\$ and external diameter of cable \$D_e\$.
• For non-magnetic armour or reinforcement, the standard defines four different scenarios for calculating the armour resistance \$R_A\$. In Cableizer, the values are more generally defined as a continuous function of the length of lay. Cableizer considers steel tape and TECK armour as touching. Steel wires are considered touching, when they cover more than 90% of the cable bedding surface. The armour resistance of touching wires is considered to be limited to 2.0 p.u., as defined in the standard for steel tape with very short lay and two or more layers of tapes in contact with each other.
Length of layTouching wires\$R_A\$ acc. IEC\$R_A\$ acc. Cableizer
very longyes or no1.0 p.u.1.0 p.u.
54° layyes or no2.0 p.u.ca. 1.7 p.u.
very shortnoinfinitelarge
very shortyes 2.0 p.u.2.0 p.u.
• For the calculation of \$λ_2\$ of single-core SL-type cable with steel wire armour, bonded to the sheath at both ends, the standard says that the loss in sheath and armour may be assumed to be approximately equal. In Cableizer, however, the loss is distributed according to the actual relation between between the screen/sheath resistance \$R_s\$ and armour resistance \$R_A\$.
• Cableizer does not only calculate the armour losses with more flexibility and precision, but does also allow both screen and sheath in the same cable, which is common for modern cables with aluminum laminated sheath and round copper wires.
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