Cable Ampacity

Are you comparing buried insulated conductors versus aerial bare conductors? Please provide actual examples if you would like realistic results.

Is this for a test, an interview question or, God Forbid, do you have a job in power industry?

In any case you should not ask others to do your work for you.

Did you check this at various ambient temperature and soil resistivities.

The maximal current through a cable depends on the resistivity which leads to heat amount/ length unit and the capability to transfer it to the environment.

Heat generation is proportional to current density x conductor area and heat transfer is proportional to contact area with environment x heat conduction / convection factors but decreases with insulating properties of the mantel. If diameter is low the ration heat transfer area to conductor are is bigger and the insulation is thinner so that convection could be preponderant.

In ground the nature of the ground and its content of water can lead to vzery different results.

In my opinion, it depends on many factors as ambient temperature, insulation and sheath, number of conductor and number of cables, the limits of "lower cross section cable" and other.

Usually up to 2 k.m./W earth thermal resistance and up to 30oC ambient it is correct up to 6 awg [16 sqr.mm copper conductor XLPE insulation].The explanation could be as follows:

The thermal flux[ equivalent] resistance will be the same in the inner part-in insulation and jacket[sheath]. What will be different is the outside thermal resistance.

Let's take IEC 60287-2-1 definitions:

1. cable in free air T4=1/(π* De* h* Δθ^0.25) ; T4=K/DeK is relatively constant then T4 decrease with the cable diameter.
2. cable in ground : T4=1/(2*π)* roT* ln(2*u) ; T4=A*[B-ln(De)]While A*[B-ln(De)]<K/De then Iground>Iair.