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

The parameter k appears in the series expansion which approximates the P and Q terms of Carson’s equations (see Equation 10 and Equation 12 of Section 2.1.1 for details). It is of the form

$k=4\pi d\sqrt{2\lambda f}$ | (20) |

where

$\lambda$ is the earth conductivity in ab℧/cm^{3}.

d is a distance in centimeters.

This can be rewritten in terms of readily available quantities (i.e. commonly published units)
by substituting earth resistivity (Ω/m^{3}) for conductivity and distance in conductor
separation units for distance in centimeters as follows

$k=4\pi d(u_{CS}\to cm)\sqrt{\frac{2\lambda f(\lambda\to\rho)}{\rho}}$ | (21) |

where

u_{CS} is conductor separation unit. In the US, conductor separation
is usually measured in feet.

u_{CS}$\to$ cm is the number of centimeters per conductor separation unit.

$\lambda\to\rho$ is a constant converting ab℧/cm^{3}
to Ω/m^{3}.

Assuming that the frequency and resitivity are constant for any set of impedance computations the bulk of the expression

$4\pi(u_{cs}\to cm)\sqrt{\frac{2\lambda f(\lambda\to\rho)}{\rho}}$ | (22) |

is a constant which is computed once then stored for reuse.

After P and Q are computed, the terms 4$\omega$P
and 4$\omega$Q in Equation
5 through Equation
8 of Section 2.1.1 produce impedances in units of abΩ/cm. If
impedances are expressed in Ω/u_{LL}, these terms expand to

$4\omega(u_{LL}\to cm)(ab\Omega\to\Omega)P$ | (23) |

and

$4\omega(u_{LL}\to cm)(ab\Omega\to\Omega)Q$ | (24) |

where

u_{LL} is line length unit. In the US, line length is usually measured in miles.

u_{CR}$\to$ cm is the number of centimeters per line length unit.

ab$\Omega\to\Omega$ is a constant converting abΩ to Ω,
i.e. 1×10^{-9}.

Assuming that the frequency is constant, both P and Q are multiplied by the same factor

$4\cdot 2\pi f(u_{ll}\to cm)(ab\Omega\to\Omega)$ | (25) |

The first terms of of the inductive reactance equations (Equation 7 and Equation 8 of Section 2.1) are also multiplied by half of this value, i.e.

$2\cdot 2\pi f(u_{ll}\to cm)(ab\Omega\to\Omega)$ | (26) |

Once again, both of these constants are calculated once then stored.

When the logarithmic term in Equation 7 of Section 2.1 is computed, the conductor’s GMR must be converted to conductor separation units, i.e.

$ln\left(\frac{2h_{i}}{gmr_{j}}\right)$ | (27) |

is actually evaluated as

$ln\left(\frac{2h_{i}}{gmr_{j}(u_{CR}\to u_{CS})}\right)$ | (28) |

where u_{CR} $\to$ u_{CS} converts
conductor radius units to conductor separation units. Factoring out a constant in this
expression yields

$ln\left(\frac{ch_{i}}{gmr_{j}}\right)$ | (29) |

where

$c=\frac{2}{u_{CR}\to u_{CS}}$ | (30) |

The factor c is also calculated once and stored.