The graphs show 10 MHz ground constants at eleven locations in Great Britain. The soil was sampled at several depths to 10′. Linear interpolation may appear curved on a log scale. Units conversion: statmho/cm → mS/m.
This writeup compares ground constants from a stratified ground model with those from surface ground probes. I model eight locations in Great Britain at one frequency and one location in Oregon at eight frequencies.
To reduce sampling artifacts, I oversample the ground constant data by a factor of 10, linearly interpolating between the original samples. Imagine the curves with tiny stairstep layers, each with uniform ground constants. Layer boundaries are halfway between oversamples, with the last layer infinitely deep. I calculate the Fresnel reflection coefficient for a plane wave vertically incident on the oversampled, stratified ground. Then I find ground constants for uniform soil that yield the same coefficient. The two ground models should be equivalent whenever the reflection coefficient is valid. I model a 12″ ground probe by averaging ground constants at the surface and 1′ below. For a 24″ probe I use a 1:2:1 weighted average of 0′, 1′, and 2′.
Location Geology Peq Ceq P12 P24 C12 C24 ■ Rugby 1 Lower lias 22 81 2.22 2.14 1.03 1.24 ■ Baldock Chalk 20 9.5 1.17 1.15 1.37 1.14 ■ Tatsfield Upper greensand 44 42 0.78 0.61 1.18 1.06 ■ Brookmans Park London clay 16 18 1.56 1.54 0.97 0.95 ■ Washford Cross Red marls 12 29 2.68 2.95 0.91 1.03 ■ Moorside Edge Millstone grit 45 34 0.85 0.81 1.15 1.02 ■ Westerglen Boulder clay 16 14 1.28 1.30 1.05 1.17 ■ Teddington London clay 24 8.4 0.57 0.55 1.86 1.63
Peq and Ceq are equivalent ground constants. P12, P24, C12, and C24 are ratios of the ground probe response to the equivalent. No equivalent exists for ■ Rugby 2, ■ Daventry, or ■ Brendon Hills.
Geometric 0.91–1.1 0.83–1.2 0.67–1.5 0.50–2.0 Error ≤ 10% ≤ 20% ≥ 50% ≥ 100% P12 0 2 4 2 P24 0 1 5 2 C12 4 6 1 0 C24 4 6 1 0
Rudy Severns, N6LF, used a 12″ ground probe and NanoVNA to measure ground constants in a newly dug trench in Oregon bottomland. He inserted the probe horizontally in the trench wall. The soil was loam down to the bottom at 6′ where it became gravel. He inserted the probe vertically at 6′ and at the surface next to the trench.
The graph shows 10.1 MHz values for the stratified ground analysis. I derived ground constants for the 3″ surface layer from the surface measurement and those at 0.5′ and 1′ it overlapped. For the deepest measurement I used the mean probe depth of 6.5′. I modeled a 24″ probe by combining measurements at the surface, 1′, and 2′. I oversampled the data by a factor of 10, but it had little effect.
MHz Peq Ceq P12 P24 C12 C24 28.5 11 39 2.12 2.68 0.73 0.96 21.2 13 37 1.91 2.42 0.68 0.90 14.2 17 33 1.61 2.05 0.65 0.87 10.1 20 32 1.54 1.95 0.62 0.83 7.1 28 31 1.21 1.53 0.57 0.77 3.7 69 26 0.61 0.76 0.60 0.82 1.8 119 17 0.45 0.54 0.79 1.11 1.0 152 13 0.42 0.50 0.95 1.36
Peq and Ceq are equivalent ground constants. P12, P24, C12, and C24 are ratios of the ground probe response to the equivalent.
Geometric 0.91–1.1 0.83–1.2 0.67–1.5 0.50–2.0 Error ≤ 10% ≤ 20% ≥ 50% ≥ 100% P12 0 0 7 3 P24 0 0 7 4 C12 1 1 4 0 C24 1 5 0 0
Fresnel reflection coefficients are valid for plane waves, but the fields near ground may not be planar for low antennas. If Sommerfeld-Norton and reflection coefficient ground differ little for a NEC antenna model, equivalent ground constants should be valid when used with the reflection coefficient method. Use calculator values to model antenna currents, impedance, and overhead gain. Equivalence may not be valid at lower elevation angles since it is derived from RF incident at 90°.
Most of the Peq values seem far from an eyeball average of the permittivity curve. But stratified ground does not average. It acts like a cascade of transmission lines. Line impedance corresponds to permittivity and line loss to conductivity.
A stratified layer may resonate. It is an artifact of sparse sampling unless the layer actually is thick. Oversampling inhibits artificial resonance. Oversampling by a factor of 10, 100, or 1000 yields virtually identical results. Use the calculator to explore transformation and resonance.
The notion of equivalent ground constants is not entirely coherent. Reduce the ground constants of the upper soil layer until they become those of air. This increases antenna height by the layer depth. But no set of equivalent ground constants can do this. In general, stratified ground requires a model more complex than NEC provides.
A ground probe samples a smaller percentage of soil with current as skin depth increases. This occurs for drier soils or lower frequencies. To assess the sampling limitation, see tabulated skin depth for the Hagn generic curves or use this program to calculate skin depth.
Geometric 0.91–1.1 0.83–1.2 0.67–1.5 0.50–2.0 Error ≤ 10% ≤ 20% ≥ 50% ≥ 100% P12 0 2 11 5 P24 0 1 12 6 C12 5 7 5 0 C24 5 11 1 0
Combined error for Great Britain and Oregon.
8″ of concrete over pastoral ground Water table 200′ below desert
This program calculates equivalent ground constants for stratified ground with two layers. The documentation includes typical permittivity and conductivity values for snow, ice, asphalt, concrete, and rock. Generic values for soil and water are here.
A high antenna excites ground with a wavefront that has already incurred appreciable spreading loss. In contrast, fields from a buried radial spread cylindrically and decay quickly. Ground current concentration near the surface should enable a ground probe to provide suitable ground constants for antennas with buried radials. This may be true for radials on the ground as well. However, subsurface soil, especially that beyond the radials, can affect ground reflection coefficients. This will limit accuracy for far-field results. But probe constants should be appropriate for studying the effect of radial number, length, and depth on antenna efficiency.
This article explains how to determine ground constants with a low dipole. Unlike a ground probe, the method excites subsurface soil. However, excitation is shallower than for a high antenna. Ground current decays more rapidly with depth because the fields are less planar. A low dipole may be insensitive at depths your antenna excites. The low-dipole method is restricted to a single band, needs a large, flat, open area free of structures, vegetation, and ground conductors, requires meticulous construction, measurement, and modeling, and must be left in place or rebuilt to measure at different seasons.
Use bare copper wire. At each end use the smallest loop possible through a tiny polystyrene insulator attached to nonconductive line. The loop/insulator affects feedpoint impedance but NEC cannot model it. Minimize wire sag and model average height. A height too low may incur error due to surface irregularity. Measure and model the excess shunt capacitance at the center insulator. Use a male-male adapter instead of a VNA cable. Record measurements without touching the VNA. Increase model segmentation until impedance converges. Recalculate the Sommerfeld-Norton interpolation grid as needed to maintain impedance accuracy. To mitigate the single-band limitation, use this program to extrapolate ground constants to other bands.
Smith-Rose, R. L., "Electrical Measurements on Soil with Alternating Currents," Proc. IEE, Vol. 75, pp. 221-237, 1934. I skipped the three locations with indefinite depths or no surface measurement.
88–108 MHz