Cross-sectional area filler

Cross-sectional area of filler

Symbol

$A_{f}$

Unit

mm$^2$

Formulas

$\pi \left(\frac{D_{f}}{2}\right)^2-2\pi {r_{core}}^2$	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]

$D_{f}$

Diameter over 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 filler [kg/m]

$Q_{f}$

Thermal capacitance filler [J/(m.K)]