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# Geometric Mean Distance

Centre to centre spacing is frequently used in cable calculations.  This is particularly obvious in the calculation of inductance. Where the spacing varies between cores (for example in flat configurations), an average spacing is used; the geometric mean distance.

## Geometric Mean Spacing

Given  known spacing between conductors, the geometric mean distance is given by:

$d=\sqrt[3]{{d}_{L1L2}{d}_{L1L3}{d}_{L2L3}}$

and

${d}_{LN}=\sqrt[3]{{d}_{L1LN}{d}_{L2LN}{d}_{L3LN}}$

where:
d             - geometric mean distance between phases, m
dn            - geometric mean distance between phase and neutral, m
LXLX        - spacing (centre to centre) between phases, m
L1L2        - between L1 and L2
L1L3        - between L1 and L3
L2L3        - between L2 and L3
L1LN        - between L1 and N
L2LN        - between L2 and N
L3LN        - between L3 and N

## Cable Configurations - Distance Between Conductors

The spacing between cores depends on the cable arrangement and configuration.  The starting point is a set of standard cable/core configurations:

 cables or cores arranged in trefoil cables or cores in flat formation (touching) cables or cores in flat formation (spaced) cable or cores in 4-core arrangement cable or cores in 5-core arrangement where: $r=\frac{d}{2*\mathrm{sin}\left(\mathrm{\pi }}{5}\right)}$ and $h=r\left[1+\mathrm{cos}\left(\mathrm{\pi }}{5}\right)\right]$ * angles are in radians

For single core cables, d is the overall diameter of the cable.  For cores of a low voltage multicore cable, d is the diameter of the core over the insulation. For medium voltage cables, d is the diameter over the insulation and including any insulation semi-conducting layer and metallic screen.

The distances given in the table are accurate for circular conductors.  For sector-shaped conductors, using the values above will result in insignificant minor variations against actual geometric mean distances.