This discussion of overhead transmission line shunt admittance concludes with a brief dicussion of computing contant factors associated with the potential matrix and reconciling units of measure while evaluating these constants.

The constant associated with the computation of potential coefficients in
Equation
33 depends only upon the medium in which the
conductors reside. Assuming that the conductors are suspended in air
($\epsilon_{r}=1$), the potential constant (in F^{-1}m) is

$\frac{1}{2\pi\epsilon_{0}\epsilon_{r}}=\frac{1}{2\pi\cdot 8.8541853\times 10^{% -12}\cdot 1}=1.79751087\times 10^{10}$ | (43) |

To compute potential coefficients in line length units rather than meters, an
additional conversion factor m $\to$ u_{LL} is required, i.e. the multiplier in
Equation
33 is actually

$\frac{m\to u_{LL}}{2\pi\epsilon}$ |

or

$(m\to u_{LL})1.79751087\times 10^{10}$ | (44) |

which produces potential coefficients with units
F^{-1} · u_{LL}. This product
is computed once and stored.

The self potential in Equation 33 is

$\frac{ln\left(\frac{D_{ii}}{d_{i}}\right)}{2\pi\epsilon}$ |

When this term is computed, the numerator and denominator of the logarithmic
factor must be in the same units. Assuming that the conductor’s diameter (in u_{CD})
is readily available, the distance must be converted to conductor
separation units and the diameter must be converted to a radius. Therefore,
the computed logarithmic factor is

$ln\left(\frac{D_{ii}}{\frac{d_{i}}{2}(u_{CD}\to u_{CS})}\right)$ |

where u_{CD} $\to$ u_{CS} converts conductor diameter to conductor separation units.

Factoring out a constant in this expression

$ln\left(c\frac{D_{ii}}{d_{i}}\right)$ | (45) |

where

$c=\frac{2}{u_{CR}\to u_{CS}}$ | (46) |

The factor c is computed once and saved.

Note: In the context of the current discussion, the clear choice of unit for
capacitive reactance is Ω · u_{LL}.
However, the capacitive reactance found in American reference materials is
often MΩ · u_{LL} or more specifically
MΩ · mile. Hence, an additional factor may be required when converting capacitive
reactance from computational units to commonly published units (ie. 10^{-6} for converting
MΩ to Ω).