Ground Modeling

TABLE 1. Bulk dielectric constants ( ε_r measured at 100 MHz) of common earth materials.
Material	ε_r (Davis and Annan, 1989)	ε_r (Daniels , 1996)
Air	1	1
Distilled water	80
Fresh water	80	81
Sea water	80
Fresh water ice	3-4	4
Sea water ice		4-8
Snow		8-12
Permafrost		4-8
Sand, dry	3-5	4-6
Sand, wet	20-30	10-30
Sandstone, dry		2-3
Sandstone, wet		5-10
Limestone	4-8
Limestone,dry		7
Limestone wet		8
Shales	5-15
Shale,wet		6-9
Silts	5-30
Clays	5-40
Clay, dry		2-6
Clay, wet		15-40
Soil, sandy dry		4-6
Soil, sandy wet		15-30
Soil, loamy dry		4-6
Soil, loamy wet		10-20
Soil, clayey dry		4-6
Soil, clayey wet		10-15
Coal, dry		3.5
Coal, wet		8
Granite	4-6
Granite, dry		5
Granite, wet		7
Salt, dry	5-6	4-7

When modelling low (< ½λ) horizontal wires in EZNEC, the Sommerfeld-Norton (real, high-accuracy) ground model must be used. The MININEC model will give inaccurate results under these conditions for both gain and impedance. It should be reserved for high antennas or verticals. However The Sommerfeld-Norton model fails for earthed conductors, that is, wires in or touching the ground, so that, for instance, it is not usually possible to model the effect of the earthy outer of a feeder for low antennas.

EZNEC needs figures both for the ground conductivity, in Siemens, and the ground dielectric constant. As can be seen from the table of dielectric constants for typical substrates at the right, ground parameters vary considerably with conditions, particularly moisture.

I have been unable to find good figures for ground conductivity. The map below, produced by QuinetiQ and republished in Practical Wireless without accreditation, is the best I can find.

ground conductivity map

In the Bristol area, average conditions may be taken as a conductivity of about 0.013S and a dielectric constant of 13 for usual weather conditions. Both these figures may be reduced to values between 6 and 10 during periods of drought.

Ground modelling