This is the loss factor caused by eddy currents for sheath bonded at a single point.

When a non-magnetic armour is present, $R_s$ is replaced by $R_e$, and $d$ is replaced by $d_e$ in the following formulas.

Symbol
$\lambda_{\mathrm{1es}}$
Unit
-
Formulae
$\frac{R_{\mathrm{s}}}{R} \left(8.33333333333333 \cdot 10^{-14} \beta_{\mathrm{1}}^{4} t_{\mathrm{sh}}^{4} + g_{\mathrm{s}} \lambda_{\mathrm{0}} \left(\Delta _{\mathrm{1}} + \Delta _{\mathrm{2}} + 1\right)\right)$single-core cables
$\frac{4.0 \cdot 10^{-14} \omega^{2} s_{\mathrm{c}}^{2}}{R R_{\mathrm{s}} d_{\mathrm{s}}^{2}} \left(1 + \frac{s_{\mathrm{c}}^{2}}{4 d_{\mathrm{s}}^{2}}\right)$two-core cables with round conductors
$\frac{1.08 \cdot 10^{-15} \omega^{2}}{R R_{\mathrm{s}} d_{\mathrm{s}}^{2}} \left(12.2 + \frac{1}{d_{\mathrm{s}}^{2}} \left(0.74 d_{\mathrm{c}} + t\right)^{2}\right) \left(0.74 d_{\mathrm{c}} + t\right)^{2}$two-core cables with sector-shaped conductors
$\frac{3 R_{\mathrm{s}}}{R} \left(\frac{4 s_{\mathrm{c}}^{2}}{3 d_{\mathrm{s}}^{2} \left(\frac{100000000000000.0 R_{\mathrm{s}}^{2}}{\omega^{2}} + 1\right)} + \frac{16 s_{\mathrm{c}}^{4}}{9 d_{\mathrm{s}}^{4} \left(\frac{400000000000000.0 R_{\mathrm{s}}^{2}}{\omega^{2}} + 1\right)}\right)$three-core cables with round conductors, $R_{\mathrm{sh}}$ <= 100μΩ/m
$\frac{4.26666666666667 \cdot 10^{-14} \omega^{2} s_{\mathrm{c}}^{2}}{R R_{\mathrm{s}} d_{\mathrm{s}}^{2}}$three-core cables with round conductors, $R_{\mathrm{sh}}$ > 100μΩ/m
$\frac{0.94 R_{\mathrm{s}} \left(d_{\mathrm{c}} + t\right)^{2}}{R d_{\mathrm{s}}^{2} \left(\frac{100000000000000.0 R_{\mathrm{s}}^{2}}{\omega^{2}} + 1\right)}$three-core cables with sector-shaped conductors
$0$otherwise
$\frac{R_{\mathrm{encl}}}{R} \left(8.33333333333333 \cdot 10^{-14} \beta_{\mathrm{1}}^{4} t_{\mathrm{encl}}^{4} + g_{\mathrm{s}} \lambda_{\mathrm{0}} \left(\Delta _{\mathrm{1}} + \Delta _{\mathrm{2}} + 1\right)\right)$GIL
Related
$\beta_{\mathrm{1}}$
$d_{\mathrm{c}}$
$d_{\mathrm{e}}$
$d_{\mathrm{s}}$
$\omega$
$R_{\mathrm{e}}$
$R_{\mathrm{encl}}$
$t_{\mathrm{encl}}$
$t_{\mathrm{sh}}$
Used in
$\lambda_{\mathrm{1e}}$