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Mean distance between the phases

This is the geometric mean distance between phases.

In case of three single-core cables in flat formation, equal distance, with regular transposition, $a_m$ becomes the equation $2 \sqrt[3]{2}\cdot s_{c}$ as it is used in IEC 60287-1-1, chapter 2.3.2.

Symbol
$a_m$
Unit
mm
Formulas
$1000D_E$single-phase system
$s_c$two-phase system
$\left(a_{12} a_{23} a_{31}\right)^{\frac{1}{3}}$three-phase system
Related
$a_{12}$
Distance phase 1 — phase 2 [mm]
$a_{23}$
Distance phase 2 — phase 3 [mm]
$a_{31}$
Distance phase 3 — phase 1 [mm]
$D_E$
Equivalent depth of earth return path [m]
$GMD$
Geometric mean distance between phases of the same system [m]
$s_c$
Separation of conductors in a system [mm]
Used in
$GMD$
Geometric mean distance between phases of the same system [m]
$H_s$
Conductance sheath [H/m]
$X_{ar}$
Self reactance armour [$\Omega$/m]
$X_e$
Self reactance screen/sheath [$\Omega$/m]
$X_{S1}$
Reactance section 1 [$\Omega$/m]
$X_{S2}$
Reactance section 2 [$\Omega$/m]
$X_{S3}$
Reactance section 3 [$\Omega$/m]