# Documentation

## References Documents

Cableizer is based on international and american standards and uses additional methods from technical publications and books.

Cableizer is based mainly upon several standards from the International Electrotechnical Commission (IEC).

• IEC 60038:2009 (Ed.7.0): Standard Voltages
• IEC 60071-1:2006-01 (Ed.8.0) + Amd1:2010: Insulation co-ordination – Part 1: Definitions, principles and rules
• IEC 60228:2004-11 (Ed.3.0): Conductors of insulated cables
• IEC 60287: Electric Cables - Calculation of the current rating
• Part 1-1:2014-11 (Ed.2.1): Current rating equations (100% load factor) and calculation of losses - General
• Part 1-3:2002-05 (Ed.1.0): Current rating equations (100% load factor) and calculation of losses - Current sharing between parallel single-core cables and calculation of circulating current losses
• Part 2-1:2015-04 (Ed.2.0): Thermal resistance - Calculation of thermal resistance
• Part 2-2:1995-05 (Ed.1.0): Thermal resistance - A method for calculating reduction factors for groups of cables in free air, protected from solar radiation
• Part 2-3:2017-04 (Ed.1.0): Thermal resistance - Cables installed in ventilated tunnels
• Part 3-1:2017-06 (Ed.2.0): Sections on operating conditions - Reference operating conditions and selection of cable type
• Part 3-3:2007-05 (Ed.1.0): Sections on operating conditions - Cables crossing external heat sources
• IEC 60502: Power cables with extruded insulation and their accessories for rated voltages from 1 kv (Um = 1,2 kv) up to 30 kv (Um = 36 kv)
• Part 1:2004 (Ed.2.0) + A1:2009: Cables for rated voltages of 1 kv (Um = 1,2 kv) and 3 kv (Um = 3,6 kv)
• Part 2:2014 (Ed.3.0): Cables for rated voltages from 6 kV (Um = 7,2 kV) up to 30 kV (Um = 36 kV)
• IEC 60840:2011 (Ed.4.0): Power cables with extruded insulation and their accessories for rated voltages above 30 kV (Um = 36 kV) up to 150 kV (Um = 170 kV) – Test methods and requirements
• IEC 60853: Electric Cables - Calculation of the cyclic and emergency current rating of cables
• Part 1:1985 (Ed.1.0) + A1:1994 + A2:2008: Cyclic rating factor for cables up to and including 18/30 (36) kV
• Part 2:1988 (Ed.1.0) + A1:2008 Cyclic rating of cables greater than 18/30 (36) kV and emergency ratings for cables of all voltages
• Part 3:2002 (Ed.1.0): Cyclic rating factor for cables of all voltages, with partial drying of the soil
• IEC 60949:1988 (Ed.1.0) + A1:2008-09: Calculation of the thermally-permissible short-circuit currents, taking into account non-adiabatic heating effects
• IEC 62067:2011 (Ed.2.0): Power cables with extruded insulation and their accessories for rated voltages above 150 kV (Um = 170 kV) up to 500 kV (Um = 550 kV) – Test methods and requirements
• IEC 62440:2008 (Ed.1.0): Electric cables with a rated voltage not exceeding 450/750 V – Guide to use
• IEC TR 62602:2009 (Draft Proposal): Conductors of insulated cables - Data for AWG and KCMIL sizes

Standard cables were designed according to recommendations in European Standards (EN) and Harmonized Documents (HD).

• EN 50525 2011: Electric cables - Low voltage energy cables of rated voltages up to and including 450/750 V (U0/U)
• DIN EN 50565-1 2015: Electric cables - Guide to use for cables with a rated voltage not exceeding 450/750 V - Part 1: General guidance
• HD 21 S1 2006 (Withdrawn): Cables of rated voltages up to and including 450/750 V and having thermoplastic insulation
• FprHD 603 S2 2016 & HD 603 S1 2010: Distribution cables of rated voltage 0,6/1 kV
• HD 620 S2 2010: Distribution cables with extruded insulation for rated voltages from 3,6/6 (7,2) kV up to and including 20,8/36 (42) kV
• HD 632 S3 2017 & SN HD 632 S2 2008: Power cables with extruded insulation and their accessories for rated voltages above 36 kV (Um = 42 kV) up to 150 kV (Um = 170 kV)

Cableizer used the standardized values for wire diameters and conductor resistances for AWG sizes from several American standards.

• ANSI UL 1581-2011: Reference Standard for Electrical Wires, Cables, and Flexible Cords
• ASTM B2-00: Standard Specification for Medium-Hard-Drawn Copper Wire
• ASTM B8-04: Standard Specification for Concentric-Lay-Stranded Copper Conductors, Hard, Medium-Hard, or Soft
• ASTM B226-04: Standard Specification for Cored, Annular, Concentric-Lay-Stranded Copper Conductors
• ASTM B231-04: Standard Specification for Concentric-Lay-Stranded Aluminum 1350 Conductors
• ASTM B258-02: Standard Specification for Standard Nominal Diameters and Cross-Sectional Areas of AWG Sizes of Solid Round Wires Used as Electrical Conductors
• ASTM B400-04: Standard Specification for Compact Round Concentric-Lay-Stranded Aluminum 1350 Conductors
• ASTM F1883-2013: Standard Practice for Selection of Wire and Cable Size in AWG or Metric Units

The User Guides from CIGRE are a good source for better understanding of electrotechnical topics and sometimes provide additional methods not published in the IEC standards.

• Guide 218_2003 Gas Insulated Transmission Lines (GIL)
• Guide 272_2005 Large cross-sections and composite screens design
• Guide 283_2005 Special Bonding of High Voltage Power Cable Systems
• Guide 338_2007 Statistics of AC underground cables in power networks
• Guide 531_2013 Cable Systems Electrical Characteristics
• Guide 559_2013 Impact of EMF on current ratings and cable systems
• Guide 606_2015 Upgrading and uprating existing cable systems
• Guide 610_2015 Offshore generation cable connections
• Guide 640_2015 A Guide for Rating Calculations of Insulated Cables
• Guide 669_2016 Mechanical forces in large cross section cables systems
• Guide 689_2017 Life cycle assessment of underground cables
• Guide 714_2017 Long term performance of soil and backfill systems
• Guide 720_2018 Fire issues for insulated cables in air
• Guide 730_2018 Dry Air, N2, CO2 and N2-SF6 Mixtures for Gas-Insulated Systems
• Guide 756_2019 Thermal monitoring of cable circuits and grid operators' use of dynamic rating systems
• Guide 797_2020 Sheath bonding systems of AC transmission cables - design, testing, and maintenance
• Guide 806_2020 Responsible management of electric and magnetic fields (EMF)

Electra provides information on the results or the progress of the technical activities of CIGRE, on the life of the Association and on the events organised.

• Elektra024_1972 Current ratings of cables for cyclic and emergency loads
• Elektra044_1976 Current ratings of cables for cyclic and emergency loads part 2
• Elektra028_1973 The design of specially bonded cable systems
• Elektra047_1976 The design of specially bonded cable systems part 2
• Elektra066_1979 The calculation of continuous ratings for forced cooled cables
• Elektra084_1982 The conditions controlling the drying-out of soil around power cables
• Elektra087_1983 A simple formula for the calculation of the convective heat transfer between conductor and sheath in compressed gas insulated (CGI) cables (Vermeer1983)
• Elektra087_1983 Computer method for the calculation of the response of single-core cables to a step function thermal transient
• Elektra092_1984 Results of questionnaire on reliability of forced cooled cable installations (plus Erratum Elektra098_1985)
• Elektra098_1985 The calculation of the effective external thermal resistance of cables laid in materials having different thermal resistivities
• Elektra100_1985 Calculation of the continuous rating of single core, rigid type, compressed gas insulated cables in still air with no solar radiation
• Elektra104_1986 Current ratings of cables buried in partially dried out soil
• Elektra104_1986 Forced cooled cables - Calculation of thermal transients and cyclic loads
• Elektra106_1986 Calculation of the continuous rating of single core, rigid type, compressed gas insulated cables in still air with solar radiation
• Elektra113_1987 The calculation of continuous rating for forced-cooled high pressure oil-filled pipe-type cables (plus Erratum Elektra119_1988)
• Elektra125_1989 Calculation of the continuous rating of three-core, rigid type, compressed gas insulated cables in still air and buried
• Elektra128_1990 Guide to the protection of specially bonded cable systems against sheath overvoltages
• Elektra128_1990 The steady state thermal behaviour of accessories for cooled cable systems
• Elektra143_1992 Calculation of temperatures in ventilated cable tunnels
• Elektra144_1992 Calculation of temperatures in ventilated cable tunnels Appendix I-IV (plus Erratum Elektra203_2003)
• Elektra145_1992 Determination of a value of critical temperature rise for a cable backfill material
• Elektra145_1992 Methods for calculating cyclic ratings for buried cables with partial drying of the surrounding soil
• Elektra156_1994 Laying and installation of high voltage extruded cable systems - Literature evaluation data comparison
• Elektra174_1997 Magnetic Field calculation in underground cable systems with ferromagnetic components
• Elektra212_4 Thermal ratings of HV cable accessories
• Elektra222_8 Special bonding of high voltage power cables
• Elektra248_3 Cable Systems in Multi Purpose or Shared Structures
• Elektra265_1 Overall cost comparison between cables and overhead lines
• Elektra271_4 Impact of EMF on current ratings
• Elektra290_1 Mechanical forces in large cross-section cables systems

Following books we consulted and can be recommended.

• Ampacity of H.V. Multi-Insulation Cables at Different Cooling Methods, by Mohammed Ramiz Almallah, Scholars' Press, 2016
• Ampacity Optimization of Unequally Loaded Power Cables, by by Wael Moutassem, VDM Verlag, 2008
• Analysis of Nonlinear Heat Transfer in Electric Cables, by Dvorsky Karl, Südwestdeutscher Verlag für Hochschulschriften AG and Company KG, 2013
• Auswahl und Bemessung von Kabeln und Leitungen, by Herbert Schmolke, Hüthig und Pflaum, 4. Auflage, 2010
• Boden und Energiewende - Trassenbau, Erdverkabelung und Erdwärme, by verschiedene Editoren, Springer Fachmedien Wiesbaden, 2015
• Bonding of Underground Single-Core Cables and Sheath Losses, by Ossama Gouda, Adel Farag, Lap Lambert Academic Publishing, 2013
• Development of a Software Package for Calculating Current Rating of Medium Voltage Power Cables, by D.G.A.K. Wijeratna, J.R. Lucas et al., University of Moratuwa, 2003
• New: Distributed Fiber Sensing and Dynamic Rating of Power Cables, by Sudhakar Cherukupalli, George Anders, IEEE Press, 2020
• EHV AC Undergrounding Electrical Power - Performance and Planning, by Roberto Benato, Antonio Paolucci, Springer-Verlag London, 2010
• Electric Cables Handbook by BICC Cables, by George F. Moore, Blackwell Science, 3. Edition 1997
• Electrical Power Cable Engineering, by William A. Thue, 1999
• Electric Power Generation, Transmission, and Distribution, by L.L. Grigsby, CRC Press, 3. Edition 2012
• Elektrische Kraftwerke und Netze, by D. Oeding, B.R. Oswald, Vieweg+Teubner Verlag, 8th Edition 2016
• Electromagnetic Transients in Power Cables, by Filipe Faria da Silva, Claus Leth Bak, Springer-Verlag London, 2013
• Symmetrische Komponenten in Drehstromsystemen, by August Hochrainer, Springer-Verlag, 1957
• Extruded Cables For High-Voltage Direct-Current Transmission - Advances in Research and Development, by G. Mazzanti, M. Marzinotto, John Wiley & Sons. 2013
• Fundamentals of heat transfer, by S.S. Kutateladze, Academic Press, 1. Edition 1963
• Handbook of Electric Power Calculations, by H. Wayne Beaty, Surya Santoso, McGraw-Hill Education, 4. edition 2015
• High-Tension Underground Electric Cables, by Henry Floy, Electrical Publishing Company, 1909
• High Voltage Engineering, by J.R. Lucas, University of Moratuwa
• Kabel und Leitungen für Starkstrom - Grundlagen und Produkt-Know-How für das Projektieren von Kabelanlagen, by L. Heinhold, R. Stubbe, Publicis Publishing, 5. Auflage 1999
• Kabelanlagen für Hoch- und Höchstspannung, by E.P. Peschke, R. v. Olshausen, Publicis MCF Verlag, 1998
• Power Line Ampacity System - Theory, Modeling, and Application, by Anjan K. Deb, CRC Press, 2000
• Rating of Electric Power Cables, by G.J. Anders, McGraw-Hill Professional, 1. Edition 1997
• Rating of Electric Power Cables in Unfavorable Thermal Environment, by G.J. Anders, Wiley-IEEE Press, 1. Edition 2005
• Submarine Power Cables, byT. Worzyk, Springer, 2009
• The Mechanics of Soils and Foundations, by John Atkinson, Taylor and Francis, 2007
• Thermal Design of Underground Systems, by B.M. Weedy, John Wiley & Sons, 1988
• Underground Power Cables, by S. Y. King, N. A. Halfter, Longman Group Ltd., 1. Edition 1982

All parameters used in Cableizer are listed below. Click on the links for more information like values, used equations and references to other parameters.

## List of parameters

The list of parameters is automatically generated from the Cableizer source code and is valid as of 2021-07-28.

Click on a parameter name in order to get more information about that specific parameter.

 Symbol Name Unit A $a_{0}$ Coefficient a for partial transient temperature rise 1/s $a_{12}$ Distance between phase 1 and 2 mm $a_{23}$ Distance between phase 2 and 3 mm $a_{31}$ Distance between phase 3 and 1 mm $A_{a}$ Cross-sectional area of armour mm$^2$ $A_{a_{1}}$ Cross-sectional area of 1st armour mm$^2$ $A_{a_{2}}$ Cross-sectional area of 2nd armour mm$^2$ $A_{ab_{1}}$ Cross-sectional area of 1st armour bedding mm$^2$ $A_{ab_{2}}$ Cross-sectional area of 2nd armour bedding mm$^2$ $A_{c}$ Cross-sectional area of conductor mm$^2$ $a_{c}$ Skin and proximity effect coefficient a for GIL conductor $A_{comp}$ Cross-sectional area of compartment m$^2$ $A_{d}$ Cross-sectional area of duct wall mm$^2$ $A_{d_{fill}}$ Free cross-sectional area inside duct mm$^2$ $A_{di}$ Surface of duct inner wall m$^2$ $A_{do}$ Surface of duct outer wall m$^2$ $A_{e}$ Surface of object m$^2$ $A_{encl}$ Cross-sectional area of enclosure mm$^2$ $a_{encl}$ Skin and proximity effect coefficient a for GIL enclosure $A_{er}$ Surface of object m$^2$ $A_{f}$ Cross-sectional area of filler mm$^2$ $A_{fluid}$ Cross-sectional area of fluid mm$^2$ $A_{i}$ Cross-sectional area of insulation mm² $A_{ins}$ Cross-sectional area of insulation mm$^2$ $A_{it}$ Cross-sectional area of insulation (IEC 60853) mm² $A_{j}$ Cross-sectional area of jacket mm$^2$ $A_{k}$ Thermal property constant A mm/s$^{1/2}$ $a_{m}$ Mean distance between the phases mm $A_{pipe}$ Cross-sectional area of fluid-filled pipe mm$^2$ $A_{prot}$ Cross-sectional area of protective cover mm$^2$ $a_{S1}$ Length of 1st section (minor) p.u. $a_{S2}$ Length of 2nd section (medium) p.u. $a_{S3}$ Length of 3rd section (major) p.u. $A_{sc}$ Cross-sectional area of screen mm$^2$ $A_{scb}$ Cross-sectional area of screen beddig mm$^2$ $A_{scs}$ Cross-sectional area of screen serving mm$^2$ $A_{sh}$ Cross-sectional area of sheath mm$^2$ $A_{shj}$ Cross-sectional area of sheath jacket mm$^2$ $a_{shj}$ Factor $a_{shj}$ for jacket around each core $A_{sp}$ Cross-sectional area of steel pipe mm$^2$ $A_{t}$ Cross-sectional area of the tunnel m$^2$ $a_{type}$ Construction of armour $\alpha_{0}$ Constant depending on the burial depth $\alpha_{ar}$ Temperature coefficient of armour material 1/K $\alpha_{at}$ Heat transfer coefficient to channel wall W/(K.m$^2$) $\alpha_{c}$ Temperature coefficient of conductor material 1/K $\alpha_{encl}$ Temperature coefficient of enclosure material 1/K $\alpha_{f}$ Phase shift ° $\alpha_{gas}$ Thermal diffusivity for gas m$^2$/s $\alpha_{M}$ Factor $\alpha_M$ $\alpha_{sa}$ Heat transfer coefficient for convection W/(K.m$^2$) $\alpha_{sc}$ Temperature coefficient of screen material 1/K $\alpha_{sh}$ Temperature coefficient of sheath material 1/K $\alpha_{sp}$ Temperature coefficient of steel pipe material 1/K $\alpha_{st}$ Heat transfer coefficient for radiation W/(K.m$^2$) $\alpha_{sys}$ Inclination angle in degrees ° $\alpha_{t}$ Conductor to surface attainment factor B $B$ Susceptance S/m $b_{0}$ Coefficient b for partial transient temperature rise 1/s $B_{1_{1}}$ Loss coefficient $B_1$ of 1st armour $\Omega$/m $B_{1_{2}}$ Loss coefficient $B_1$ of 2nd armour $\Omega$/m $B_{2_{1}}$ Loss coefficient $B_2$ of 1st armour $\Omega$/m $B_{2_{2}}$ Loss coefficient $B_2$ of 2nd armour $\Omega$/m $b_{c}$ Skin and proximity effect coefficient b for GIL conductor $B_{EMF}$ Magnetic field strength $\mu$T $b_{encl}$ Skin and proximity effect coefficient b for GIL enclosure $B_{k}$ Thermal property constant B mm$^2$/s $b_{\mathrm{Nu}_{r}}$ Factor b $b_{shj}$ Factor $b_{shj}$ for jacket around each core $b_{x}$ Shorter side of backfill mm $b_{y}$ Longer side of backfill mm $\beta_{0}$ Constant $\beta_0$ (Ovuworie) $\beta_{1}$ Substitution coefficient $\beta_1$ for eddy-currents $\beta_{6}$ Factor $|1-\beta(6)|$ $\beta_{a_{1}}$ Angle between armour and cable axis rad $\beta_{a_{2}}$ Angle between 2nd armour and cable axis rad $\beta_{air}$ Volumetric thermal expansion coefficient of air 1/K $\beta_{ar}$ Reciprocal of temperature coefficient of armour material K $\beta_{b}$ Angle of exposed wetted surface of pipe rad $\beta_{c}$ Reciprocal of temperature coefficient of conductor material K $\beta_{encl}$ Reciprocal of temperature coefficient of enclosure material K $\beta_{gas}$ Volumetric thermal expansion coefficient for gas 1/K $\beta_{k}$ Reciprocal of temperature coefficient of resistance K $\beta_{M}$ Factor $\beta_M$ $\beta_{sc}$ Reciprocal of temperature coefficient of screen material K $\beta_{sh}$ Reciprocal of temperature coefficient of sheath material K $\beta_{sp}$ Reciprocal of temperature coefficient of steel pipe material K $\beta_{t}$ Attainment factor cable surface to ambient $\beta_{X}$ Crossing angle [rad] rad $\beta_{xing}$ Crossing angle [°] ° $\mathrm{Bi}_{g}$ Biot number of the ground $\mathrm{Bi}_{p}$ Biot number of the pipe C $C_{av}$ Heat capacity of the air flow W/K $C_{b}$ Capacitance of insulation F/m $C_{b3}$ Factor C3 for partially buried pipes $C_{bq}$ Constants $C_1$ - $C_7$ of multi-layer backfill $C_{c1}$ Thermal capacitance, 1st loop J/m.K $C_{c2}$ Thermal capacitance, 2nd loop J/m.K $C_{c3}$ Thermal capacitance, 3rd loop J/m.K $C_{c4}$ Thermal capacitance, 4th loop J/m.K $c_{color}$ Wiring color code $C_{g1}$ Factor C1 for partially buried pipes $C_{g2}$ Factor C2 for partially buried pipes $c_{gas}$ Constant c for a gas under GIL conditions $c_{ij}$ Coefficient c for view factor $C_{k1}$ Non-adiabatic constant $C_1$ mm/m $C_{k2}$ Non-adiabatic constant $C_2$ K.m.mm$^2$/J $C_{\mathrm{Nu}_{L}}$ Factor C $c_{\mathrm{Nu}_{r}}$ Factor c $C_{\mathrm{Nu}_{w}}$ Factor C $c_{p_{gas}}$ Specific heat capacity at constant pressure J/kg.K $c_{p_{soil}}$ Specific heat capacity of soil J/kg.K $c_{p_{w}}$ Specific heat capacity at constant pressure J/kg.K $c_{shj}$ Factor $c_{shj}$ for jacket around each core $c_{SI}$ Surge velocity of propagation km/s $c_{type}$ Construction of conductor $c_{v_{gas}}$ Specific heat capacity at constant volume J/kg.K $c_{v_{w}}$ Specific heat capacity at constant volume J/kg.K $C_{vair}$ Volumetric heat capacity of air J/K.m$^3$ $CC$ Charging capacity kvar/km $CC_{pull}$ Conduit clearance mm $CF_{pull}$ Conduit fill $\%$ $CJ_{pull}$ Conduit jamming ratio $cos\varphi$ Power factor $CR_{pull}$ Conduit ratio $cuw$ Standard copper wires mm D $d_{a}$ Mean diameter of armour mm $d_{a_{1}}$ Mean diameter of 1st armour mm $D_{a_{1}}$ External diameter of 1st armour mm $d_{a_{2}}$ Mean diameter of 2nd armour mm $D_{a_{2}}$ External diameter of 2nd armour mm $D_{ab_{1}}$ Diameter over 1st armour bedding mm $D_{ab_{2}}$ Diameter over 2nd armour bedding mm $d_{b}$ Diameter of the backfill mm $d_{b3}$ Distance c of multi-layer backfill m $d_{b4}$ Distance d of multi-layer backfill m $d_{c}$ External diameter of conductor mm $D_{c}$ Diameter of conductor m $d_{ci}$ Internal diameter of conductor mm $D_{comp}$ Diameter of compartment (metric) m $d_{comp}$ Diameter of compartment mm $d_{ct}$ External diameter of conductor for transient calculations mm $D_{di}$ Inner diameter of duct m $D_{do}$ Outer diameter of duct m $D_{dry}$ Diameter of drying zone m $D_{e}$ External diameter of object mm $d_{e}$ Diameter of sheath and armour mm $d_{encl}$ Outer diameter of enclosure mm $D_{encl}$ Outer diameter of enclosure (metric) m $D_{eq}$ Equivalent diameter of a group of cables mm $D_{ext}$ Overall outer diameter of pipe m $D_{f}$ External diameter of the filler mm $d_{f}$ Spacing from hottest object in group m $d_{f_{1}}$ Thickness of 1st armour mm $d_{f_{2}}$ Thickness of 2nd armour mm $D_{i}$ Diameter over insulation mm $d_{im}$ Imaginary layer of soil m $D_{in}$ Inner diameter of pipe m $D_{ins}$ Diameter over insulation without insulation screen mm $d_{ins}$ Diameter of insulation around pipe mm $D_{it}$ Diameter over insulation for transient calculations mm $d_{j}$ Diameter below jacket m $D_{o}$ Outer diameter m $d_{pk1}$ Distance to mirrored buried object mm $d_{pk2}$ Distance between buried objects mm $d_{prot}$ Diameter of protective cover mm $d_{psc}$ Point source correction m $D_{ref}$ Reference diameter for determination of OHTC m $d_{s}$ Mean diameter of screen/sheath mm $D_{sc}$ Diameter over screen mm $d_{sc}$ Mean diameter of screen mm $D_{scb}$ Diameter over screen bedding mm $D_{scs}$ Diameter over screen serving mm $D_{sh}$ External diameter of sheath mm $d_{sh}$ Mean diameter of sheath mm $D_{shb}$ Diameter below sheath mm $D_{shj}$ Diameter of sheath jacket m $D_{soil}$ Outer diameter of soil layer m $d_{t}$ Channel covering m $d_{w}$ Depth under water m $D_{wall}$ Outer diameter of steel pipe m $d_{x}$ Equivalent diameter of a conductor mm $D_{x}$ Characteristic diameter mm $D_{x_{w}}$ Characteristic diameter for weekly load mm $D_{x_{y}}$ Characteristic diameter for yearly load mm $\Delta _{1}$ Substitution coefficient $\Delta_1$ for eddy-currents $\delta _{1}$ Thickness of screening layer mm $\Delta _{2}$ Substitution coefficient $\Delta_2$ for eddy-currents $\delta _{ar}$ Equivalent thickness of armour mm $\delta _{d}$ Distance between cable and duct m $\delta _{k}$ Thickness of screen, sheath or armour mm $\delta _{soil}$ Soil thermal diffusivity m$^2$/s $\Delta d_{sh}$ Depth of corrugation mm $\Delta H_{c}$ Heat of combustion coefficient MJ/kg $\Delta t$ Length of time step s $\Delta \theta_{0t}$ Air temperature in tunnel increase K $\Delta \theta_{0x}$ Temperature rise by crossing heat sources K $\Delta \theta_{0x_{1}}$ Temperature rise of the conductor, first estimate K $\Delta \theta_{0x_{h}}$ Temperature rise of the conductor by source h K $\Delta \theta_{a_{t}}$ Corrected transient temperature rise of conductor K $\Delta \theta_{air}$ Temperature increase of air K $\Delta \theta_{c}$ Temperature rise of conductor K $\delta \theta_{c}$ Ohmic steady-state temperature rise K $\Delta \theta_{c_{t}}$ Transient temperature rise of conductor by ohmic losses K $\Delta \theta_{ce}$ Temperature difference, conductor to surface K $\Delta \theta_{d}$ Temperature rise by dielectric losses K $\Delta \theta_{e_{t}}$ Transient temperature rise of outer surface K $\Delta \theta_{gas}$ Temperature difference, conductor to enclosure °C $\Delta \theta_{kp}$ Temperature rise by buried object k K $\Delta \theta_{max}$ Maximum permissible conductor temperature rise K $\Delta \theta_{p}$ Temperature rise by other buried objects K $\Delta \theta_{R}$ Conductor temperature rise above ambient temperature K $\Delta \theta_{R_{\infty}}$ Maximum permissible conductor temperature rise °C $\Delta \theta_{s}$ Temperature difference surface to ambient K $\delta \theta_{SPK}$ Peak cyclic temperature rise K $\Delta \theta_{sun}$ Temperature rise by solar radiation K $\Delta \theta_{t}$ Transient temperature rise of conductor K $\Delta \theta_{t_{\infty}}$ Steady-state temperature rise of conductor K $\Delta \theta_{x}$ Critical soil temperature rise K $\Delta \theta_{x0}$ VDE soil temperature rise K $\Delta W$ Incremental heat generated W $\Delta z$ Length of the interval m $Di_{d}$ Inner diameter of duct mm $di_{pipe}$ Internal diameter of fluid-filled pipe mm $Di_{sp}$ Inner diameter of steel pipe mm $Di_{t}$ Tunnel inner diameter m $Do_{d}$ Outer diameter of duct mm $do_{pipe}$ External pipe diameter mm $Do_{sp}$ Outer diameter of steel pipe mm $Do_{t}$ Tunnel/trough outer diameter m E $E_{bs}$ Installation constant E $e_{hor}$ Horizontal clearance mm $e_{limit}$ Limit of thickness of soil layer m $e_{soil}$ Thickness of soil layer m $E_{stress}$ Electrical field strength kV/mm $e_{ver}$ Vertical clearance mm $e_{wall}$ Clearance to wall mm $EEC$ Embodied energy and carbon MJ/kg $\epsilon_{0}$ Vacuum permittivity F/m $\epsilon_{c}$ Effective emissivity of conductor $\epsilon_{di}$ Emissivity of duct inner surface $\epsilon_{do}$ Emissivity of duct outer surface $\epsilon_{e}$ Emissivity of cable surface $\epsilon_{encl}$ Effective emissivity of enclosure $\epsilon_{gas}$ Dielectric constant of gas in compartment $\epsilon_{i}$ Relative permittivity of insulation $\epsilon_{k}$ Heat loss allowance factor $\epsilon_{prot}$ Effective emissivity of protective cover $\epsilon_{rad}$ Effective emissivity $\eta0_{gas}$ Reference dynamic viscosity of gas Pa.s $\eta_{di}$ Reflectivity of (opaque) duct inner surface $\eta_{do}$ Reflectivity of (opaque) duct outer surface $\eta_{e}$ Reflectivity of (opaque) cable surface $\eta_{gas}$ Dynamic viscosity of gas Pa.s $\eta_{w}$ Dynamic viscosity of water Pa.s F $f$ System frequency Hz $F_{a_{1}}$ Effective length per unit lay length of 1st armour mm $F_{a_{2}}$ Effective length per unit lay length of 2nd armour mm $F_{\alpha}$ Inclination derating factor p.u. $f_{atm}$ Relation atmospheric pressure to standard atmosphere $f_{cb}$ Factor for cross-bonded earthing $F_{e}$ Factor $F_e$ for eddy-current losses $F_{eq}$ Factor for envelope circle for a group of cables $F_{form}$ Form factor $F_{g}$ Gravitational force daN/m $F_{ij}$ View factor object-object $F_{k}$ Imperfect contact thermal factor $F_{m}$ Radiation coefficient mutual $F_{mh}$ Mutual heating coefficient $f_{ppc}$ Factor of permissible pull N/mm$^2$ $F_{ppc}$ Permissible pull force daN $F_{pt}$ Function of pressure and temperature $F_{pull}$ Pulling force daN $f_{rad}$ Sidewall bearing pressure factor N/m $F_{rad}$ Sidewall bearing pressure daN/m $F_{red}$ Reduction factor for the permissible current rating $f_{SHF}$ Sheath factor $F_{T10_{1}}$ Factor Table 10, single cables p.u. $F_{T10_{3}}$ Factor Table 10, trefoil groups p.u. $F_{T11_{s}}$ Factor Table 11, first part p.u. $F_{T11_{t}}$ Factor Table 11, second part p.u. $F_{T12}$ Factor Table 12 p.u. $F_{T13}$ Factor Table 13 p.u. $f_{wc}$ Weight correction factor $F_{x}$ Geometrical distance factor for multi-core cables G $g$ Standard acceleration of gravity m/s$^2$ $G$ Conductance S/m $G_{1}$ Geometric factor $G_1$ $G_{2}$ Geometric factor $G_2$ for cables with separate sheaths $g_{a}$ Substitution coefficient g $G_{b}$ Geometric factor for backfill $g_{bs}$ Installation constant g $G_{corr}$ Geometric correction factor $G_{corr}$ for jacket around each core $g_{dry}$ Geometric constant of circle with dried-out soil p.u. $G_{encl}$ Factor G for the calculation of the Nusselt number $G_{FEA}$ Geometric reference factor $G_{FEA}$ based on FEM fitting $G_{od}$ Aspect ratio object/duct $g_{s}$ Substitution coefficient $g_s$ for eddy-currents $G_{s00}$ Factor $G_{s 0.0}$ $G_{s05}$ Factor $G_{s 0.5}$ $G_{s10}$ Factor $G_{s 1.0}$ $g_{x}$ Geometric constant of circle with characteristic diameter p.u. $\gamma_{a}$ Armour angle rad $\gamma_{bessel}$ Bessel constant p.u. $\gamma_{c}$ Skin and proximity effect factor $\gamma$ for GIL conductor $\gamma_{encl}$ Skin and proximity effect factor $\gamma$ for GIL enclosure $\gamma_{euler}$ Euler's constant m/s$^2$ $\gamma_{t}$ Attainment factor for groups of cables $\gamma_{X}$ Attenuation factor for crossing 1/m $GMD$ Geometric mean distance mm $GMR$ Geometric mean radius mm $\mathrm{Gr}_{c}$ Grashof number, conductor to gas $\mathrm{Gr}_{da}$ Grashof number, duct in air $\mathrm{Gr}_{encl}$ Grashof number, gas to enclosure $\mathrm{Gr}_{gd}$ Grashof number, gas to duct $\mathrm{Gr}_{L}$ Grashof number, ground to air $\mathrm{Gr}_{od}$ Grashof number, object to duct $\mathrm{Gr}_{og}$ Grashof number, object to gas $\mathrm{Gr}_{prot}$ Grashof number, surface to air H $H$ Distance center of pipe to ground m $h_{1}$ Factor $h_1$ for emergency load $H_{1_{1}}$ Component of inductance $H_1$ of 1st armour H/m $H_{1_{2}}$ Component of inductance $H_1$ of 2nd armour H/m $H_{2_{1}}$ Component of inductance $H_2$ of 1st armour H/m $H_{2_{2}}$ Component of inductance $H_2$ of 2nd armour H/m $H_{3_{1}}$ Component of inductance $H_3$ of 1st armour H/m $H_{3_{2}}$ Component of inductance $H_3$ of 2nd armour H/m $h_{amb}$ Pseudo film coefficient of ambient fluid at ground level W/(K.m$^2$) $h_{atm}$ Height above sea level m $h_{b}$ Height of the backfill mm $h_{bs}$ Heat dissipation coefficient for black surfaces in free air W/m$^2$/K$^{5/4}$ $h_{buried}$ Heat transfer coefficient wall to soil W/(K.m$^2$) $H_{c}$ Heat energy content MJ/m $h_{c}$ Convection heat transfer coefficient, conductor to gas W/(K.m$^2$) $h_{conv_{da}}$ Convection heat transfer coefficient, duct to air W/(K.m$^2$) $h_{conv_{gd}}$ Convection heat transfer coefficient, gas to duct W/(K.m$^2$) $h_{conv_{od}}$ Convection heat transfer coefficient, object to duct W/(K.m$^2$) $h_{conv_{og}}$ Convection heat transfer coefficient, object to gas W/(K.m$^2$) $h_{conv_{sa}}$ Convection heat transfer coefficient, surface to air W/(K.m$^2$) $h_{encl}$ Convection heat transfer coefficient, gas to enclosure W/m2.K $h_{era}$ Convection heat transfer coefficient acc. ERA W/(K.m$^2$) $h_{ext}$ External heat transfer coefficient W/(K.m$^2$) $h_{ground}$ Heat transfer coefficient buried part of wall to soil W/(K.m$^2$) $h_{in}$ Heat transfer coefficient inside W/(K.m$^2$) $h_{lg}$ Ratio of heat dissipation coefficients $h_{rad_{ce}}$ Radiation heat transfer coefficient, conductor to enclosure W/(K.m$^2$) $h_{rad_{da}}$ Radiation heat transfer coefficient, duct to air W/(K.m$^2$) $h_{rad_{od}}$ Radiation heat transfer coefficient, object to duct W/(K.m$^2$) $h_{rad_{sa}}$ Radiation heat transfer coefficient, surface to air W/(K.m$^2$) $H_{s}$ Sheath conductance H/m $h_{soil}$ Heat transfer coefficient wall-soil W/(K.m$^2$) $H_{sun}$ Intensity of solar radiation W/m$^2$ $h_{t}$ Inner height m $h_{T4}$ Ratio of thermal resistance to ambient $H_{tc}$ Parameter H for trough $h_{tr}$ Heat transfer coefficient W/(K.m$^2$) $H_{ts}$ Parameter H depending on air velocity $H_{x}$ Magnetic field x-component mH $H_{y}$ Magnetic field y-component mH I $I_{1}$ Steady-state current before transient A $I_{2}$ Emergency load current A $I_{c}$ Conductor current A $I_{C}$ Capacitive load current A/km $I_{c_{max}}$ Highest current load of line A $I_{c_{peak}}$ Permissible peak cyclic load current A $I_{Ce}$ Capacitive earth short-circuit current A/km $I_{EMF}$ Phase current for EMF calculation A $I_{k}$ Permissible short-circuit current kA $I_{k1}$ Phase-to-ground short-circuit current kA $I_{k2}$ Phase-to-phase short-circuit current kA $I_{k3}$ Three-phase symmetric short-circuit current kA $I_{kAD}$ Short-circuit current (adiabatic) kA $I_{kSC}$ Effective short-circuit current kA $I_{method}$ Current calculation method $I_{R}$ Transient conductor current A $inst_{air}$ Installation in air $inst_{elec}$ Installation of cables for electrical calculations $inst_{riser}$ Installation of cables in riser $inst_{sea}$ Installation of subsea cables $inst_{t}$ Installation in air inside a room J $j_{max}$ Phase angle range ° K $K$ Screening factor $K_{0}$ Coefficient K for a gas under GIL conditions $K_{02}$ Factor $K_{0.2}$ $K_{06}$ Factor $K_{0.6}$ $K_{10}$ Factor $K_{1.0}$ $k_{4}$ Thermal conductivity of soil W/(m.K) $K_{A}$ Coefficient K to calculate in air $k_{air}$ Thermal conductivity of air W/(m.K) $K_{BICC}$ Constant relating to conductor formation $k_{Boltzmann}$ Boltzmann constant J/K $k_{c}$ Thermal conductivity of conductor material K.m/W $K_{ce}$ Radiation shape factor, conductor to enclosure $K_{cv}$ Convection factor $k_{encl}$ Thermal conductivity of enclosure W/(m.K) $k_{fluid}$ Thermal conductivity of fluid W/(m.K) $k_{gas}$ Thermal conductivity for gas W/(m.K) $K_{GMR}$ Geometric mean radius factor $k_{H}$ Heinhold characteristic diameter coefficient $k_{ins}$ Thermal conductivity of insulation W/(m.K) $K_{k}$ Specific short-circuit parameter A.s$^{1/2}$/mm$^2$ $k_{l}$ Temperature rise factor in air $k_{LF}$ Load loss constant coefficient p.u. $K_{od}$ Diameter ratio object/duct $k_{p}$ Proximity effect coefficient $K_{par}$ Constant $K_{par}$ (Ovuworie) $k_{pipe}$ Thermal conductivity of fluid-filled pipe W/(m.K) $k_{prot}$ Thermal conductivity of protective cover W/(m.K) $K_{r}$ Radiation shape factor within duct $k_{r2}$ Temperature rise ratio $\delta\theta_{SPK}/\delta\theta_c$ p.u. $k_{s}$ Skin effect coefficient $k_{sa}$ Convection factor (Heinhold) $k_{sa_{1}}$ Factor 1 for convection heat transfer coefficient $k_{sa_{2}}$ Factor 2 for convection heat transfer coefficient $k_{t}$ Temperature rise ratio p.u. $K_{t}$ Effective emissivity of surface $K_{vermeer}$ Vermeer constant for convection heat transfer $k_{w}$ Thermal conductivity of water W/(m.K) $K_{x}$ Factor for fictitious diameter by Neher $k_{X}$ Number of heat sources crossing L $L_{0}$ Reference length of the tunnel m $L_{1}$ Inductance of phase 1 H/m $L_{2}$ Inductance of phase 2 H/m $L_{3}$ Inductance of phase 3 H/m $L_{b}$ Vertical center of backfill mm $L_{b4}$ Trench depth of multi-layer backfill m $L_{c}$ Depth of laying of sources mm $L_{char}$ Characteristic length earth surface $L_{cm}$ Depth of laying m $L_{crit}$ Critical system length km $L_{d}$ Length of duct m $L_{deep}$ Equivalent depth for deep burial m $L_{dry}$ Depth of characteristic diameter of drying zone m $L_{dw}$ Length of duct in water m $L_{earth}$ Equivalent depth of earth return path mm $L_{h}$ Depth of laying of crossing element mm $L_{leg}$ Length of a section m $L_{r}$ Depth of laying of the rated object mm $L_{sys}$ System length km $L_{T}$ Length of the tunnel m $\lambda_{0}$ Substitution coefficient $\lambda_0$ for eddy-currents $\lambda_{1}$ Loss factor of screen and sheath $\lambda_{1c}$ Loss factor by circulating currents $\lambda_{1cb}$ Loss factor for solid bonding $\lambda_{1e}$ Loss factor by eddy currents $\lambda_{1es}$ Loss factor for single point bonding $\lambda_{2}$ Loss factor of armour $\lambda_{3}$ Loss factor of steel pipes for pipe-type cables $\lambda_{4}$ Loss factor of ducts $\lambda_{d}$ Factor for dielectric losses $\lambda_{gas}$ Ratio $c_p/c_v$ $\lambda_{t}$ Relaxation parameter $LF$ Load factor p.u. $LF_{w}$ Weekly load factor p.u. $LF_{y}$ Yearly load factor p.u. $LME$ London Metal Exchange USD/mt M $M$ Cyclic rating factor p.u. $m_{0}$ Substitution coefficient $m_0$ for eddy-currents Hz.m/$\Omega$ $M_{0}$ Coefficient M for partial transient temperature rise s $M_{1}$ Corrected cyclic rating factor K $m_{a_{1}}$ Mass of 1st armour kg/m $m_{a_{2}}$ Mass of 2nd armour kg/m $M_{ab}$ Material of armour bedding $m_{ab_{1}}$ Mass of 1st armour bedding kg/m $m_{ab_{2}}$ Mass of 2nd armour bedding kg/m $M_{c}$ Material of conductor $m_{c}$ Mass of conductor kg/m $M_{cable}$ List of materials in a cable $M_{comp}$ Material of insulating gas $M_{d}$ Material of duct pipe $M_{e}$ Substitution coefficient $M_e$ to calculate factor $F_e$ $m_{EMF}$ Number of time steps $M_{encl}$ Material of enclosure $M_{f}$ Material of filler $m_{f}$ Mass of filler kg/m $M_{fluid}$ Fluid material $M_{gas}$ Gas and gas-mixtures $M_{i}$ Material of insulation $m_{i}$ Mass of insulation kg/m $M_{IEEE}$ Materials acc. IEEE 442 $M_{ins}$ Material of insulation around pipe $M_{j}$ Material of jacket $m_{j}$ Mass of jacket kg/m $M_{k}$ Thermal contact factor s$^{1/2}$ $M_{mol}$ Molar mass g/mol $m_{mol}$ Molecular mass mol $m_{\mathrm{Nu}_{L}}$ Factor m $m_{\mathrm{Nu}_{w}}$ Factor m $M_{pipe}$ Material of fluid-filled pipe $M_{prot}$ Material of protective cover $M_{riser}$ Material of riser $M_{s}$ Factor $M_s$ $M_{sc}$ Material of screen $m_{sc}$ Mass of metallic screen kg/m $m_{scb}$ Mass of screen bedding tapes kg/m $m_{scs}$ Mass of screen serving tapes kg/m $M_{seabed}$ Material of seabed $M_{sh}$ Material of sheath $m_{sh}$ Mass of metallic sheath kg/m $M_{shj}$ Material of sheath jacket $m_{shj}$ Mass of jacket over each core kg/m $M_{soil}$ Type of soils $M_{sp}$ Material of containment for pipe-type cables $M_{spf}$ Steel pipe filling medium $m_{tot}$ Mass of cable kg/m $\mu$ Loss factor p.u. $\mu_{0}$ Vacuum permeability H/m $\mu_{dyn}$ Dynamic friction coefficient $\mu_{e}$ Longitudinal relative permeability $\mu_{s}$ Relative permeability $\mu_{t}$ Traverse relative permeability of steel wires $\mu_{w}$ Loss factor for weekly load variation p.u. $\mu_{y}$ Loss factor for yearly load variation p.u. N $N_{0}$ Coefficient N for partial transient temperature rise s$^2$ $n_{a_{1}}$ Number of wires of 1st armour $n_{a_{2}}$ Number of wires of 2nd armour $N_{Avogrado}$ Avogadro constant 1/mol $N_{b}$ Number of loaded objects in backfill $n_{c}$ Number of conductors in object $N_{c}$ Number of sources in system $n_{cc}$ Number of conductors combined $n_{cg}$ Number of conductors in GIL $n_{cw}$ Number of wires in conductor $n_{cycle}$ Number of load cycles $N_{e}$ Substitution coefficient $N_e$ to calculate factor $F_e$ $n_{\mathrm{Nu}_{r}}$ Factor n $N_{sea}$ Number of subsea cables $N_{sum}$ Total number of objects in an air-filled space $n_{sw}$ Number of screen wires $N_{sys}$ Number of parallel systems in the same confinement $N_{X}$ Number of intervals $u$ Summation step 1 - $N_X$ $u_{air}$ Kinematic viscosity for air m$^2$/s $\mathrm{Nu}_{c}$ Nusselt number, conductor to gas $\mathrm{Nu}_{da}$ Nusselt number, duct to air $\mathrm{Nu}_{encl}$ Nusselt number, gas to enclosure $u_{gas}$ Kinematic viscosity for gas m$^2$/s $\mathrm{Nu}_{gd}$ Nusselt number, gas to duct $\mathrm{Nu}_{L}$ Nusselt number, ground to air $\mathrm{Nu}_{od}$ Nusselt number, object to duct $\mathrm{Nu}_{og}$ Nusselt number, object to gas $\mathrm{Nu}_{prot}$ Nusselt number, surface to air $u_{sc}$ Elongation of screen $\%$ $u_{soil}$ Soil moisture content $\%$ $\mathrm{Nu}_{w}$ Nusselt number, surface to water $u_{w}$ Kinematic viscosity for water m$^2$/s O $\omega$ Angular frequency rad/s P $p_{a_{1}}$ Length of lay of 1st armour mm $p_{a_{2}}$ Length of lay of 2nd armour mm $p_{ab1}$ Factor apportioning the 1st armour bedding $p_{ab2}$ Factor apportioning the 2nd armour bedding $p_{atm}$ Atmospheric air pressure hPa $p_{cb}$ Minor ratio of section lengths $P_{cc}$ Substitution coefficient P to calculate loss factor by circulating currents $p_{comp}$ Gas pressure in compartment bar $p_{gas}$ Gas pressure Pa $p_{i}$ Factor apportioning the insulation $p_{j}$ Factor apportioning the jacket $P_{L}$ Active power at load receptor kW $p_{\mathrm{Nu}_{r}}$ Factor p $p_{shj}$ Factor apportioning the sheath jacket $p_{soil}$ Depth of image source $p_{tr}$ Effective perimeter of trough m $p_{w}$ Water pressure bar $\Phi_{air}$ Relative humidity of air $\%$ $\phi_{arc}$ Angle of a bend rad $\phi_{el}$ Angle to the plane of a section rad $\phi_{tr}$ Parameter $\phi$ for trough $\pi$ Archimedes' constant $\pi$ $\mathrm{Pr}_{air}$ Prandtl number for air $\mathrm{Pr}_{gas}$ Prandtl number for gas $\mathrm{Pr}_{w}$ Prandtl number for liquids Q $q_{1}$ Ratio of losses affecting screen bedding/serving $q_{2_{1}}$ Ratio of losses affecting 1st armour bedding $q_{2_{2}}$ Ratio of losses affecting 2nd armour bedding $q_{3}$ Ratio of losses affecting jacket $q_{4}$ Ratio of losses affecting environment $q_{a}$ Ratio of losses armour $Q_{A}$ Element A of two-part thermal circuit J/m.K $Q_{a_{1}}$ Thermal capacitance of 1st armour J/m.K $Q_{a_{2}}$ Thermal capacitance of 2nd armour J/m.K $Q_{ab_{1}}$ Thermal capacitance of 1st armour bedding J/m.K $Q_{ab_{2}}$ Thermal capacitance of 2nd armour bedding J/m.K $Q_{B}$ Element B of two-part thermal circuit J/m.K $Q_{B_{ab1}}$ Element B of two-part thermal circuit of 1st armour bedding J/m.K $Q_{B_{ab2}}$ Element B of two-part thermal circuit of 2nd armour bedding J/m.K $Q_{B_{d}}$ Element B of two-part thermal circuit, duct J/m.K $Q_{B_{f}}$ Element B of two-part thermal circuit, filler J/m.K $Q_{B_{i}}$ Element B of two-part thermal circuit, insulation J/m.K $Q_{B_{j}}$ Element B of two-part thermal circuit, jacket J/m.K $Q_{B_{s}}$ Element B of two-part thermal circuit, screen/sheath J/m.K $Q_{c}$ Thermal capacitance of conductor J/m.K $q_{cb}$ Major ratio of section lengths $Q_{cc}$ Substitution coefficient Q to calculate loss factor by circulating currents $Q_{ct}$ Thermal capacitance of conductor (IEC 60853) J/m.K $Q_{d}$ Thermal capacitance of duct wall J/m.K $Q_{d_{fill}}$ Thermal capacitance of duct filling J/m.K $Q_{f}$ Thermal capacitance of filler J/m.K $q_{f}$ Ratio of losses affecting the filler $Q_{i}$ Thermal capacitance of insulation J/m.K $Q_{it}$ Thermal capacitance of insulation (IEC 60853) J/m.K $Q_{it1}$ Thermal capacitance of insulation, 1st portion (IEC 60853) J/m.K $Q_{it2}$ Thermal capacitance of insulation, 2nd portion (IEC 60853) J/m.K $Q_{j}$ Thermal capacitance of jacket J/m.K $Q_{s}$ Thermal capacitance of screen+sheath J/m.K $q_{s}$ Ratio of losses screen/sheath $Q_{sc}$ Thermal capacitance of screen J/m.K $Q_{scb}$ Thermal capacitance of screen bedding J/m.K $Q_{scs}$ Thermal capacitance of screen serving J/m.K $Q_{sh}$ Thermal capacitance of sheath J/m.K $Q_{shj}$ Thermal capacitance of sheath jacket J/m.K $Q_{sp}$ Thermal capacitance of steel pipe J/m.K $Q_{tot}$ Total thermal capacitance, transient J/m.K $q_{x}$ Factor for characteristic diameter R $R_{0}$ Zero sequence resistance $\Omega$/m $R_{1}$ Resistance of conductor before emergency rating $\Omega$/m $R_{A}$ Electrical resistance of armour $\Omega$/m $R_{A_{1}}$ Electrical resistance of 1st armour $\Omega$/m $R_{A_{2}}$ Electrical resistance of 2nd armour $\Omega$/m $r_{arc}$ Radius of a bend m $r_{b}$ Equivalent radius of backfill mm $r_{c}$ Radius of conductor mm $R_{c}$ Resistance of conductor $\Omega$/m $R_{c1}$ Thermal resistance, 1st loop K.m/W $R_{c2}$ Thermal resistance, 2nd loop K.m/W $R_{c3}$ Thermal resistance, 3rd loop K.m/W $R_{c4}$ Thermal resistance, 4th loop K.m/W $R_{CG}$ Thermal resistance of multi-layer backfill K.m/W $R_{co}$ DC resistance of conductor at 20°C $\Omega$/m $R_{e}$ Electrical resistance of sheath and armour $\Omega$/m $R_{e_{1}}$ Electrical resistance of sheath and 1st armour $\Omega$/m $R_{e_{2}}$ Electrical resistance of sheath and 2nd armour $\Omega$/m $R_{earth}$ Equivalent resistance of earth return path p.u. $R_{encl}$ Electrical resistance of enclosure $\Omega$/m $R_{encl20}$ DC resistance of enclosure at 20°C $\Omega$/m $r_{F}$ Radius below the insulation mm $R_{gas}$ Specific gas constant J/kg.K $R_{gas0}$ Universal molar gas constant $r_{I}$ Radius of the insulation mm $r_{ij}$ Coefficient r for view factor $R_{max}$ Resistance of conductor at emergency rating $\Omega$/m $r_{mbi}$ Minimal bending radius for installation m $r_{mbif}$ Factor of minimal installation bending radius $r_{mbp}$ Minimal bending radius during cable pulling m $r_{mbpf}$ Factor of minimal pulling bending radius $r_{o}$ Radius of object m $R_{q11}$ Thermal resistance 11 of multi-layer backfill K.m/W $R_{q12}$ Thermal resistance 12 of multi-layer backfill K.m/W $R_{q13}$ Thermal resistance 13 of multi-layer backfill K.m/W $R_{q21}$ Thermal resistance 21 of multi-layer backfill K.m/W $R_{q22}$ Thermal resistance 22 of multi-layer backfill K.m/W $R_{q31}$ Thermal resistance 31 of multi-layer backfill K.m/W $R_{q32}$ Thermal resistance 32 of multi-layer backfill K.m/W $R_{s}$ Electrical resistance of screen$||$sheath $\Omega$/m $R_{sc}$ Electrical resistance of screen $\Omega$/m $R_{sh}$ Electrical resistance of sheath $\Omega$/m $R_{so}$ Resistance of screen and sheath at 20°C $\Omega$/m $R_{sp}$ Electrical resistance of steel pipe $\Omega$/m $r_{x}$ Radius to point x in insulation mm $\mathrm{Ra}_{c}$ Rayleigh number, conductor to gas $\mathrm{Ra}_{encl}$ Rayleigh number, gas to enclosure $\mathrm{Ra}_{gas}$ Rayleigh number gas/duct $\mathrm{Ra}_{L}$ Rayleigh number, ground to air $\mathrm{Ra}_{prot}$ Rayleigh number, surface to air $\mathrm{Re}_{air}$ Reynolds number for air $\mathrm{Re}_{w}$ Reynolds number for water $RF$ Reduction factor $\rho_{4}$ Thermal resistivity of soil K.m/W $\rho_{4d}$ Thermal resistivity of dry soil K.m/W $\rho_{ab}$ Thermal resistivity of armour bedding K.m/W $\rho_{ab_{2}}$ Thermal resistivity of bedding between armour layers K.m/W $\rho_{ar}$ Specific electrical resistivity of armour material $\Omega$.m $\rho_{b}$ Thermal resistivity backfill K.m/W $\rho_{b1}$ Thermal resistivity of surface layer K.m/W $\rho_{b2}$ Thermal resistivity of middle layer K.m/W $\rho_{c}$ Electrical resistivity of conductor material $\Omega$.m $\rho_{corr}$ Thermal resistivity of corrugation filling K.m/W $\rho_{cr}$ Thermal resistivity of conductor material K.m/W $\rho_{d}$ Thermal resistivity of duct material K.m/W $\rho_{d_{fill}}$ Thermal resistivity of bentonite filling K.m/W $\rho_{earth}$ Specific electrical resistivity of soil $\Omega$.m $\rho_{encl}$ Specific electrical resistivity of enclosure material $\Omega$.m $\rho_{f}$ Thermal resistivity of filler K.m/W $\rho_{gas}$ Gas density kg/m$^3$ $\rho_{i}$ Thermal resistivity of insulation K.m/W $\rho_{j}$ Thermal resistivity of jacket material K.m/W $\rho_{k2}$ Thermal resistivity of the layer located above K.m/W $\rho_{k20}$ Electrical resistivity of metallic component $\Omega$.m $\rho_{k3}$ Thermal resistivity of the layer located below K.m/W $\rho_{ki}$ Thermal resistivity of adjacent material K.m/W $\rho_{m}$ Thermal resistivity of the screen K.m/W $\rho_{sc}$ Specific electrical resistivity of screen material $\Omega$.m $\rho_{scb}$ Thermal resistivity of screen bedding K.m/W $\rho_{scs}$ Thermal resistivity of screen serving K.m/W $\rho_{sh}$ Specific electrical resistivity of sheath material $\Omega$.m $\rho_{shj}$ Thermal resistivity of sheath jacket material K.m/W $\rho_{sp}$ Specific electrical resistivity of steep pipe material $\Omega$.m $\rho_{t}$ Thermal resistivity of wall K.m/W $\rho_{w}$ Density of water kg/m$^3$ S $s_{air}$ Axial spacing between objects m $s_{b1}$ Thickness of surface layer m $s_{b2}$ Thickness of middle layer m $s_{b3}$ Thickness from object to top of bedding layer m $s_{b4}$ Thickness from object to bottom of bedding layer m $s_{c}$ Separation of conductors in a system mm $s_{cm}$ Separation of conductors in a system m $S_{G}$ Apparent power at injecting point kVA $S_{gas}$ Sutherland's constant K $s_{ij}$ Spacing between object i and j $S_{k}$ Cross-sectional area of current carrying component mm$^2$ $s_{S1}$ Spacing between phases in 1st section p.u. $s_{S2}$ Spacing between phases in 2nd section p.u. $s_{S3}$ Spacing between phases in 3rd section p.u. $SI$ Surge Impedance $\Omega$ $\sigma$ Stefan Boltzmann constant W/m$^2$K$^4$ $\sigma_{ab}$ Volumetric heat capacity of armour bedding J/K.m$^3$ $\sigma_{ab_{2}}$ Volumetric heat capacity of bedding between armour layers J/K.m$^3$ $\sigma_{ar}$ Volumetric heat capacity of armour material J/K.m$^3$ $\sigma_{c}$ Volumetric heat capacity of conductor material J/K.m$^3$ $\sigma_{d}$ Volumetric heat capacity of duct material J/K.m$^3$ $\sigma_{d_{fill}}$ Volumetric heat capacity of duct filling J/K.m$^3$ $\sigma_{encl}$ Volumetric heat capacity of enclosure material J/K.m$^3$ $\sigma_{f}$ Volumetric heat capacity of filler J/K.m$^3$ $\sigma_{fluid}$ Volumetric heat capacity of fluid J/K.m$^3$ $\sigma_{i}$ Volumetric heat capacity of insulation material J/K.m$^3$ $\sigma_{ins}$ Volumetric heat capacity of insulation J/K.m$^3$ $\sigma_{j}$ Volumetric heat capacity of jacket material J/K.m$^3$ $\sigma_{k2}$ Specific isobaric volumetric heat capacity of layer located below J/K.m$^3$ $\sigma_{k3}$ Volumetric heat capacity of layer located above J/K.m$^3$ $\sigma_{kc}$ Volumetric heat capacity of metallic component J/K.m$^3$ $\sigma_{ki}$ Volumetric heat capacity of adjacent material J/K.m$^3$ $\sigma_{pipe}$ Volumetric heat capacity of fluid-filled pipe J/K.m$^3$ $\sigma_{prot}$ Specific isobaric volumetric heat capacity of protective cover J/K.m$^3$ $\sigma_{sc}$ Volumetric heat capacity of screen material J/K.m$^3$ $\sigma_{scb}$ Volumetric heat capacity of screen bedding J/K.m$^3$ $\sigma_{scs}$ Volumetric heat capacity of screen serving J/K.m$^3$ $\sigma_{sh}$ Volumetric heat capacity of sheath material J/K.m$^3$ $\sigma_{shj}$ Volumetric heat capacity of sheath jacket material J/K.m$^3$ $\sigma_{sp}$ Volumetric heat capacity of steel pipe material J/K.m$^3$ $\sigma_{sun}$ Absorption coefficient of solar radiation T $T0_{gas}$ Gas reference temperature K $T_{1}$ Thermal resistance between one conductor and sheath K.m/W $t_{1}$ Thickness of insulation to sheath mm $t_{1t}$ Thickness of insulation to sheath, transient mm $T_{2}$ Thermal resistance between sheath and armour K.m/W $t_{2}$ Thickness of bedding under armour mm $T_{2_{1}}$ Thermal resistance of 1st armour bedding K.m/W $T_{2_{2}}$ Thermal resistance of 2nd armour bedding K.m/W $t_{2i}$ Thickness of insulation between conductors mm $T_{3}$ Thermal resistance of jacket K.m/W $t_{3}$ Thickness of serving over armour mm $T_{4d}$ Transient thermal resistance for daily load K.m/W $T_{4db}$ Correction of thermal resistance for backfill K.m/W $T_{4i}$ Thermal resistance of medium in the duct K.m/W $T_{4ii}$ Thermal resistance of the duct wall K.m/W $T_{4iii}$ Thermal resistance to ambient K.m/W $T_{4\mu}$ Thermal resistance to ambient K.m/W $T_{4ss}$ Steady-state thermal resistance K.m/W $T_{4t}$ Equivalent thermal resistance for tunnel K.m/W $T_{4w}$ Transient thermal resistance for weekly load K.m/W $T_{4y}$ Transient thermal resistance for yearly load K.m/W $T_{A}$ Element A of equivalent thermal circuit K.m/W $T_{a}$ Star thermal resistance of air K.m/W $T_{a0}$ Apparent thermal resistance a K.m/W $t_{ab_{1}}$ Thickness of 1st armour bedding mm $T_{ab_{1}}$ Thermal resistance of 1st armour bedding K.m/W $t_{ab_{2}}$ Thickness of armour separation mm $T_{ab_{2}}$ Thermal resistance of 2nd armour bedding K.m/W $T_{air}$ Absolute air temperature K $T_{at}$ Thermal resistance by convection, air to tunnel K.m/W $T_{axial}$ Axial thermal resistance due to the movement of air through the tunnel K.m/W $T_{B}$ Element B of equivalent thermal circuit K.m/W $T_{b0}$ Apparent thermal resistance b K.m/W $T_{bulk}$ Bulk temperature K $t_{c}$ Thickness of hollow conductor mm $T_{C}$ Element C of equivalent thermal circuit K.m/W $t_{comp}$ Thickness of compartment mm $T_{conv_{ce}}$ Thermal resistance by convection, conductor to enclosure K.m/W $T_{conv_{sa}}$ Thermal resistance by convection, surface to air K.m/W $t_{corr}$ Thickness of corrugation filling mm $t_{cs}$ Thickness of conductor shield mm $t_{ct}$ Thickness of conductor tape mm $T_{d}$ Internal thermal resistance for dielectric losses K.m/W $t_{d}$ Thickness of duct mm $T_{e}$ External thermal resistance of tunnel K.m/W $t_{EMF}$ Time step to calculate current source s $t_{encl}$ Thickness of enclosure mm $T_{eq}$ Equivalent thermal resistance K.m/W $t_{f}$ Thickness of filler/belt insulation mm $T_{gas}$ Absolute gas temperature K $T_{i}$ Thermal resistance of insulation K.m/W $t_{i}$ Thickness of insulation mm $t_{icore}$ Thickness of core insulation mm $t_{ins}$ Thickness of insulation mm $T_{ins}$ Thermal resistance of insulation K.m/W $T_{int}$ Internal thermal resistance for current losses K.m/W $t_{is}$ Thickness of insulation screen mm $T_{is}$ Thermal resistance of insulation screen K.m/W $t_{j}$ Thickness of jacket mm $T_{j}$ Thermal resistance of jacket K.m/W $t_{jj}$ Thickness of additional layer over jacket mm $T_{jtube}$ Thermal resistance of J-tubes in air K.m/W $t_{k}$ Duration of short-circuit s $T_{L}$ Thermal longitudinal resistance K.m/W $T_{mh}$ Mutual thermal resistance between rated and crossing object K.m/W $T_{mh_{v}}$ Mutual thermal resistance per slice K.m/W $T_{o}$ Thermal resistance of the oil in the pipe K.m/W $T_{platform}$ Thermal resistance of individual phases on platform K.m/W $t_{prot}$ Thickness of protective cover mm $T_{prot}$ Thermal resistance of protective cover K.m/W $T_{r}$ Total thermal resistance K.m/W $T_{rad_{ce}}$ Radiation thermal resistance, conductor to enclosure K.m/W $T_{rad_{sa}}$ Radiation thermal resistance, surface to air K.m/W $T_{rad_{sun}}$ Solar radiation thermal resistance K.m/W $T_{s}$ Star thermal resistance of object K.m/W $T_{sa}$ Thermal resistance by convection, surface to air K.m/W $t_{sc}$ Thickness of the screen mm $t_{scb}$ Thickness of screen bedding mm $T_{scb}$ Thermal resistance of screen bedding K.m/W $t_{scs}$ Thickness of screen serving mm $T_{scs}$ Thermal resistance of screen bedding K.m/W $t_{sh}$ Thickness of the sheath mm $t_{sha}$ Total thickness between separate sheath and armour $t_{shj}$ Thickness of sheath jacket mm $T_{shj}$ Thermal resistance of sheath jacket K.m/W $t_{sp}$ Thickness of steel pipe mm $T_{st}$ Radiation thermal resistance, surface to tunnel K.m/W $T_{surf}$ Absolute surface temperature K $t_{t}$ Wall thickness m $T_{t}$ Star thermal resistance of tunnel K.m/W $T_{tot}$ Total thermal resistance, transient K.m/W $T_{tr}$ Thermal resistance of trough K.m/W $T_{tw}$ Thermal resistance of tunnel wall K.m/W $T_{wall}$ Thermal resistance of pipe wall K.m/W $T_{water}$ Thermal resistance of J tubes below sea level K.m/W $\mathrm{tan}\delta _{i}$ Loss factor of insulation $\tau$ Transient load period s $\tau_{L}$ Transient load period for deep burial s $\theta_{2K}$ Temperature rise for 2K criterion °C $\theta_{a}$ Ambient temperature °C $\theta_{abs}$ Absolute temperature K $\theta_{air}$ Ambient air temperature °C $\theta_{ar}$ Temperature of armour °C $\theta_{ar_{1}}$ Temperature of 1st armour °C $\theta_{ar_{2}}$ Temperature of 2nd armour °C $\theta_{at}$ Air temperature with load °C $\theta_{at_{0}}$ Air temperature with no load °C $\theta_{at_{i}}$ Air temperature of previous iteration cycle °C $\theta_{at_{L}}$ Air temperature in tunnel at outlet °C $\theta_{at_{z}}$ Air temperature in tunnel at z °C $\theta_{c}$ Temperature of conductor °C $\theta_{c_{z}}$ Conductor temperature at z °C $\theta_{cmax}$ Max. conductor temperature °C $\theta_{cmaxeo}$ Max. emergency overload conductor temperature °C $\theta_{cmaxsc}$ Max. short-circuit conductor temperature °C $\theta_{de}$ Temperature of duct outer wall °C $\theta_{di}$ Temperature of duct inner wall °C $\theta_{dm}$ Mean temperature of the medium in the duct °C $\theta_{e}$ External temperature of the object °C $\theta_{encl}$ Temperature of enclosure °C $\theta_{f}$ Temperature of filler for multi-core cables type SS with sheath °C $\theta_{film}$ Film temperature °C $\theta_{gas}$ Gas temperature °C $\theta_{hs}$ Temperature of heat source °C $\theta_{kf}$ Final temperature °C $\theta_{ki}$ Initial temperature °C $\theta_{kmax}$ Maximal temperature of non-insulation material °C $\theta_{max}$ Temperature of conductor at end of emergency loading °C $\theta_{o}$ Outer surface temperature °C $\theta_{o_{L}}$ Temperature of the surface of object at outlet °C $\theta_{o_{z}}$ Temperature of the surface of object at z °C $\theta_{omax}$ Max. outer surface temperature °C $\theta_{R}$ Rated current transient to steady-state ratio $\theta_{s}$ Temperature of screen/sheath °C $\theta_{sc}$ Temperature of screen °C $\theta_{sh}$ Temperature of sheath °C $\theta_{sp}$ Temperature of steel pipe °C $\theta_{spf}$ Mean temperature of the medium in the steel pipe °C $\theta_{surf}$ Surface temperature °C $\theta_{t}$ Temperature of inner tunnel wall °C $\theta_{t_{L}}$ Temperature of tunnel wall at outlet °C $\theta_{t_{z}}$ Temperature of tunnel wall at z °C $\theta_{tm}$ Mean temperature between surface and air in tunnel or trough °C $\theta_{to}$ Temperature of outer tunnel wall °C $\theta_{to_{z}}$ Temperature of outer tunnel wall at z °C $\theta_{w}$ Water temperature °C $\theta_{x}$ Critical soil temperature °C $TQ$ Cable thermal time constant s U $u$ Substitution coefficient u $U_{0}$ Base voltage for tests kV $u_{b}$ Substitution coefficient u $U_{buried}$ OHTC of fully buried pipe W/(K.m$^2$) $U_{d}$ Constant U for cables in ducts K.m/W $U_{e}$ Line-to-ground voltage kV $U_{exposed}$ OHTC of part of pipe in contact with water W/(K.m$^2$) $U_{ground}$ OHTC of part of pipe in contact with ground W/(K.m$^2$) $U_{inwall}$ OHTC of inside film and pipe wall W/(K.m$^2$) $U_{m}$ Highest voltage for equipment kV $U_{n}$ Rated line-to-line voltage kV $U_{o}$ Operating voltage kV $U_{OHTC}$ Overall heat transfer coefficient W/(K.m$^2$) $U_{partially}$ OHTC of partially buried pipe W/(K.m$^2$) $U_{sp}$ Constant U for pipe-type cables K.m/W $U_{ti}$ Circumference of inner rectangular tunnel wall m $U_{wall}$ OHTC of pipe wall W/(K.m$^2$) V $v_{4}$ Ratio thermal resistivity dry/moist soil $V_{air}$ Air velocity m/s $V_{comp}$ Gas volume m$^3$ $V_{d}$ Constant V for cables in ducts K.m/W $V_{drop}$ Voltage drop V/A/km $V_{fluid}$ Velocity of fluid cm/s $V_{gas}$ Volume percentage of second gas $\%$ $V_{sp}$ Constant V for pipe-type cables K.m/W $V_{w}$ Velocity of water cm/s W $W_{A}$ Armour losses W/m $W_{a_{L}}$ Heat removed by air at outlet W/m $W_{a_{z}}$ Heat removed by air at z W/m $w_{b}$ Width of the backfill mm $w_{b4}$ Distance to lateral edge of multi-layer backfill m $W_{c}$ Conductor losses W/m $W_{conv_{ce}}$ Convection heat transfer, conductor to enclosure W/m $W_{conv_{da}}$ Convection heat transfer, duct to air W/m $W_{conv_{gd}}$ Convection heat transfer, gas to duct W/m $W_{conv_{od}}$ Convection heat transfer, object to duct W/m $W_{conv_{og}}$ Convection heat transfer, object to gas W/m $W_{conv_{sa}}$ Convection heat transfer, surface to air W/m $W_{d}$ Dielectric losses W/m $W_{de}$ Losses outside of riser/J-tube W/m $W_{di}$ Losses between cable and riser/J-tube W/m $W_{duct}$ Losses in duct W/m $W_{encl}$ Enclosure losses W/m $w_{f_{1}}$ Width of flat wires of 1st armour mm $w_{f_{2}}$ Width of flat wires of 2nd armour mm $W_{h}$ Heat generated by external object W/m $W_{hs}$ Heat dissipation of heat source W/m $W_{I}$ Ohmic losses per phase W/m $W_{rad_{ce}}$ Radiation heat transfer, conductor to enclosure W/m $W_{rad_{da}}$ Radiation heat transfer, duct to air W/m $W_{rad_{od}}$ Radiation heat transfer, object to duct W/m $W_{rad_{sa}}$ Radiation heat transfer, surface to air W/m $W_{s}$ Screen and sheath losses W/m $W_{sA}$ Total loss in sheath and armour W/m $W_{sA_{1}}$ Total loss in sheath and 1st armour W/m $W_{sA_{2}}$ Total loss in sheath and 2nd armour W/m $w_{sc}$ Width of flat screen wire mm $W_{sp}$ Losses in steel pipe W/m $W_{sum}$ Sum of total losses of all systems W/m $W_{sun}$ Solar radiation heat transfer to surface W/m $W_{sys}$ Total losses of the system W/m $W_{t}$ Total losses per phase W/m $w_{t}$ Inner width m $W_{tot}$ Total losses per object W/m X $X_{0}$ Zero sequence reactance $\Omega$/m $x_{b}$ Horizontal center of backfill mm $X_{c}$ Self reactance of conductor $\Omega$/m $X_{G}$ Factor $X_G$ $X_{G2}$ Factor $X_{G2}$ $X_{K}$ Factor $X_K$ $X_{m}$ Mutual reactance between cables $\Omega$/m $x_{p}$ Factor for proximity effect of conductors $x_{pos}$ Horizontal x-position of multi-layer backfill m $x_{s}$ Factor for skin effect on conductor $X_{s}$ Self reactance of 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 $\xi_{cb}$ Parameter $\xi$ for calculation of loss factor Y $Y$ Admittance S/m $y_{2K}$ Depth for 2K criterion mm $y_{c}$ Skin and proximity effect factor for GIL conductor $Y_{d}$ Constant Y for cables in ducts K.m/W $y_{encl}$ Skin and proximity effect factor for GIL enclosure $Y_{G}$ Factor $Y_G$ $Y_{i}$ Ordinates of the loss-load cycle p.u. $Y_{K}$ Factor $Y_K$ $y_{p}$ Proximity effect factor of conductors $y_{s}$ Skin effect factor of conductor $Y_{sp}$ Constant Y for pipe-type cables K.m/W Z $Z_{0}$ Zero sequence impedance $\Omega$/m $Z_{bs}$ Installation constant Z $Z_{c}$ Self impedance of phase conductor $\Omega$/m $z_{c}$ Factor z to calculate skin effect coefficients for conductor $z_{encl}$ Factor z to calculate skin effect coefficients for enclosure $z_{h}$ Location of the heat source m $Z_{K}$ Factor $Z_K$ $Z_{m}$ Mutual impedance between conductor and metal screen $\Omega$/m $z_{max}$ Logitudinal thermal limit distance m $Z_{neg}$ Negative sequence impedance $\Omega$/m $Z_{pos}$ Positive sequence impedance $\Omega$/m $z_{r}$ Location of the hottest point m $Z_{s}$ Self impedance of metal screen $\Omega$/m $Z_{x}$ Equivalent mutual impedance between cables $\Omega$/m $\zeta_{ab}$ Density of armour bedding material g/cm$^3$ $\zeta_{ar}$ Density of armour material g/cm$^3$ $\zeta_{c}$ Density of conductor material g/cm$^3$ $\zeta_{f}$ Density of filler material g/cm$^3$ $\zeta_{i}$ Density of insulation material g/cm$^3$ $\zeta_{j}$ Density of jacket material g/cm$^3$ $\zeta_{M}$ Density of material g/cm$^3$ $\zeta_{od}$ Radiation shape factor for touching cables $\zeta_{sc}$ Density of metallic screen material g/cm$^3$ $\zeta_{scb}$ Density of screen bedding tapes g/cm$^3$ $\zeta_{scs}$ Density of screen serving tapes g/cm$^3$ $\zeta_{sh}$ Density of metallic sheath material g/cm$^3$ $\zeta_{shj}$ Density of jacket material over each core g/cm$^3$ $\zeta_{soil}$ Soil density kg/m$^3$