# Thermal resistance to ambient

Thermal resistance to ambient of a single cable or duct depends on laying.

For touching cables or ducts, different formulae are being used.

• Metallic sheathed cables are taken to be cables where it can be assumed that there is a metallic layer that provides an isotherm at, or immediately under, the outer sheath of the cable or for metallic ducts.
• Cables of the same system are assumed to be touching, when they are located at a distance smaller than 10H of their diameter. In the same way, two ducts are assumed to be touching, when they are closer than 5% of their diameter. Touching of cables from different systems is not adressed
• When the cables or ducts are embedded in concrete (backfill), the thermal resistivity of soil $\rho_4$ is replaced with the thermal resistivity of the bank material $\rho_b$ in the equations below.
• The formulas for buried cables, touching, flat formation, are valid for u >= 5 and in trefoil formation for u >= 4.
• For three buried single-core cables in touching trefoil formation, metallic sheathed or part-metallic covered, the thermal resistance of the serving over the sheath or armour, $T_3$, shall be multiplied by a factor of 1.6. Can be deactivated in the advanced options.
• For part-metallic covered cables (where helically laid armour or screen wires cover from 20 to 50% of the cable circumference), the thermal resistance of the insulation $T_1$, shall be multiplied by the factor 1.07 for cables up to 35 kV and by 1.16 for cables from 35 kV to 150 kV. Can be deactivated in the advanced options.

For cables in a channel acc. Heinhold, the thermal resistance to ambient is the total convection and radiation thermal resistance between cable and channel (Heinhold equation 18.103).

Note: $ln(g_{u})=ln(u+\sqrt{u^2-1})=\cosh^{-1}u$

Symbol
$T_{4iii}$
Unit
K.m/W
Formulae
 $\frac{\rho_4}{2\pi} \left(\ln\left(g_u\right)+\ln\left(F_{mh}\right)\right)$ 1 buried cable/duct non-touching, or with drying-out, or with cyclic loading $\frac{\rho_4}{\pi} \left(\ln\left(g_u\right)-0.451\right)$ 2 buried cables/ducts, flat touching, metallic sheathed $\frac{\rho_4}{\pi} \left(\ln\left(g_u\right)-0.295\right)$ 2 buried cables/ducts, flat touching, non-metallic sheathed $\rho_4 \left(0.475\ln\left(g_u\right)-0.346\right)$ 3 buried cables/ducts, flat touching, metallic sheathed $\rho_4 \left(0.475\ln\left(g_u\right)-0.142\right)$ 3 buried cables/ducts, flat touching, non-metallic sheathed $3\frac{\rho_4}{2\pi} \left(\ln\left(g_u\right)-0.63\right)$ 3 buried cables/ducts, trefoil touching, (part-)metallic sheathed $\frac{\rho_4}{2\pi} \left(\ln\left(g_u\right)+2\ln\left(u\right)\right)$ 3 buried cables/ducts, trefoil touching, non-metallic sheathed $\frac{1}{\pi D_o h_{bs} {\Delta \theta_s}^{\frac{1}{4}}}$ cylinders in air/trough $\frac{h_{T4}}{\pi D_o h_{bs} {\Delta \theta_s}^{\frac{1}{4}}}$ multiple groups of cylinders in air/trough $\frac{1}{\frac{1}{R_{CG,L}}+\frac{1}{R_{CG,R}}}$ cables in multi-layer backfill $\frac{1}{\frac{1}{T_{sa}+T_{at}}+T_{st}}$ Cables in channel (Heinhold) $\frac{\theta_e-\theta_a}{W_{conv,sa}+W_{rad,sa}-W_{sun}}$ PAC/GIL in air $\frac{1}{\pi D_{ext} U_{OHTC}}$ subsea $\frac{\theta_{de}-\theta_{air}}{W_{conv,ext}+W_{rad,ext}-W_{sun}}$ riser in air $\frac{1}{\pi D_{do} \left(h_{conv,ext}+h_{rad,ext}\right)}$ riser in air IEC 60287
Related
$D_{do}$
$D_{ext}$
$D_o$
$\Delta \theta_s$
$T_{at}$
$T_{sa}$
$T_{st}$
$\theta_a$
$\theta_{air}$
$\theta_{de}$
$\theta_e$
$U_{OHTC}$
$W_{conv,ext}$
$W_{conv,sa}$
$W_{rad,ext}$
$W_{rad,sa}$
$W_{sun}$
Used in
$\Delta \theta_c$
$\delta \theta_c$
$\Delta \theta_d$
$\Delta \theta_{duct}$
$\Delta \theta_s$
$\Delta \theta_{sun}$
$I_c$
$T_{4db}$
$T_{4ss}$
$T_C$
$T_{eq}$
$\theta_e$
$\theta_{hsj}$
$W_{hs}$