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Cross-sectional area of filler

Symbol
$A_f$
Unit
mm$^2$
Formulae
$\pi \left(\frac{D_f}{2}\right)^2-2\pi {r_{core}}^2$Two-core cables, round conductors
$\pi \left(\frac{D_f}{2}\right)^2-3\pi {r_{core}}^2+\frac{\sqrt{3}}{4} {D_{core}}^2-3\frac{{r_{core}}^2}{2} \left(\frac{\pi}{3}-sin\left(\frac{\pi}{3}\right)\right)$Three-core cables, round conductors
$\pi \left(\frac{D_f}{2}\right)^2-4\pi {r_{core}}^2+{D_{core}}^2-4\frac{{r_{core}}^2}{2} \left(\frac{\pi}{2}-sin\left(\frac{\pi}{2}\right)\right)$Four-core cables, round conductors
$\pi \left(\frac{D_f}{2}\right)^2-5\pi {r_{core}}^2+\frac{{D_{core}}^2}{4} \sqrt{25+10\sqrt{5}}-5\frac{{r_{core}}^2}{2} \left(\frac{2\pi}{3}-sin\left(\frac{2\pi}{3}\right)\right)$Five-core cables, round conductors
$\pi \left(\frac{D_f}{2}\right)^2-\pi \left(\frac{D_f}{2}\right)^2-\pi \left(\frac{D_f}{2}-t_f\right)^2$Multi-core cables, sector-shaped conductors (approximation)
Related
$D_{core}$
Diameter over core cable [mm]
$D_f$
External diameter of the filler [mm]
$\pi$
Archimedes' constant $\pi$
$r_{core}$
Radius over core cable [mm]
$t_f$
Thickness of filler/belt insulation [mm]
Used in
$m_f$
Mass of filler [kg/m]
$Q_f$
Thermal capacitance of filler [J/(m.K)]