Propagation
Propagation Analysis Software

# Groundwave Propagation vs. Pathlength & Frequency for Various Terrains

Author: R.J.Edwards G4FGQ © 31st August 2002

Both transmitting and receiving antennas are verticals, height = 1/4-wavelength or less, above a system of buried radial wires. A 1/2-wave vertical has 1 dB more gain than a short vertical. A 5/8-wave vertical has 1.6 dB more gain.

Predictions are valid at frequencies up to 15 or 20 MHz and at higher frequencies if there are not many obstructions along the path with heights of the order of 1/4 wavelength or greater and the landscape is fairly flat, no steep hills.

Total dB loss between transmitter output and receiver input is the sum of the basic spreading loss along the path, loss due to currents induced in the ground by the passing wave, diffraction over the horizon due to Earth curvature and antenna radiating and receiving inefficiencies including feedline losses, etc.

Distance to the radio horizon, approximately 80/Cube-root(MHz) Km, is where diffraction loss begins to take effect. Up to the horizon the Earth is assumed flat. Diffraction loss in dB increases in proportion to path length and to the cube-root of frequency. It is also affected by the type of terrain. This program assumes antennas are ground-mounted and only a small part of the path is line-of-sight.

Basic or spreading loss is proportional to path length measured in wavelengths. It increases by 6 dB, or 1 S-unit, each time the path length doubles. Computed basic loss in this program includes power gain of both transmitter and receiver antennas relative to isotropic. Gain above isotropic = 3 times = 4.77 dB for each antenna.

Impedance of the ground is measured in units of Ohm*metres. An ohm*metre is the resistance between opposite faces of a 1-metre cube of the soil. Soil has a -ve impedance angle which can be represented by a capacitance in parallel with the resistive component. The capacitance is that between 1 metre square plates, one metre apart, when the soil has a permittivity of K relative to air.

Soil impedance decreases as the fraction of organic relative to rocky material increases. It decreases rapidly as the water content increases and as amounts of ionic salts dissolved in the water increase. It has a negative temperature coefficient and impedance rises to very high values as water content freezes. Impedance decreases with increasing frequency due to the shunt capacitance.

It is not essential for the program user to know R and K of the ground - select the type of terrain from the list which best fits the average of the different types which may exist along a particular path. Propagation below 1 MHz is very insensitive to the value of K. So below 1 MHz if the R value is known enter any type of terrain which has that R value. K is of consequence above 3 or 4 MHz.

Terrain Types with Crude Estimates of Ground Resistivity and Permittivity
Terrain TypeRK
Perfectly conducting ground01
Salt seas, oceans, remote from river estuaries0.2280
Agricultural plains, warm, moist, dark fertile soil2530
Temperate climate, rainfall, steppes, pampas, prairies4025
Pastoral, undulating, damp, fertile soil, streams, trees6020
Farmland, undulating, woods, fields, grasslands, cattle10017
Flat, marshy, slow streams, grasses, weeds, bushes15015
Undulating, drier but some streams, woods, medium soil20014
Hilly, some forests, grasses, weeds, poor clay soil30013
Fairly dry climate, grasses, poor sandy stony soil50012
Dry climate, hilly, poor soil, towns and villages70011
Suburban, low-rise houses, roads, gardens, parks, pools100010
Hilly, rocky, semi-desert, small rainfall, some plants15008
City blocks, roads, streets, industrial areas, rivers20006
High-rise city blocks, spaghetti road systems, railways40005
Mountainous regions, bare rock, vegetation in valleys60004
Arid sand deserts, minimal plant and animal life150003
Unpolluted deep fresh water lakes, weeds, fish, birds100080
Note correlation between R and K except for freshwater lakes and estuaries.

Crude Estimation of Radiating Efficiency of
Short Vertical Antennas at LF

Radiating (and receiving) efficiency = Rr/(Rr+Rg+Rc)*100% where Rr = radiation resistance = 37*Square(Tangent(Phi/2)) ohms, Phi = angular height of antenna, Rg = loss ohms looking into the ground radial system, Rc = the loss resistance of the tuning/matching coil = coil reactance divided by coil Q. Coil reactance = antenna capacitive reactance which increases as antenna height decreases.

As the efficiency equation implies, in the most simple tuning/matching circuit Rr, Rg and Rc are effectively all in series. For a given antenna, receive efficiency = transmit efficiency. At LF, for a small receive coil Q=25 to 70. Large transmit coil Q=150 to 400.

A 1" diameter ground rod, 6-feet deep, in soil with resistivity 100 ohm*metres, Rg = 50 ohms. For 8 radials, 10awg, 30 feet long, buried 4 inches, Rg = 5 ohms. For other soil resistivities loss resistance Rg varies directly in proportion.

The input capacitance of an 8-foot vertical antenna, 1/3-inch diameter, is 25pF with a reactance of 1680 ohms at 3.8 MHz and 47,000 ohms at 136 kHz.

The efficiency of the 8-foot antenna when used for receiving at 3.8 MHz, tuned against the ground rod is approximately 0.5 percent. At 136 KHz it is only 0.00005%. For other lengths and frequencies vary the above in appropriate proportions. For more accurate efficiency estimates use other programs by the same author.

Reference field strength for groundwave prediction is300 millivolts per metre at a distance of 1 km from a transmitter which radiates 1 kilowatt from a short vertical antenna over a flat lossless ground, subject to the condition that the ground-path distance is greater than 3 or 4 wavelengths.

"Short" means 1/4-wave or less in height, i.e., at heights at which radiation in the vertical plane is proportional to the cosine of the angle of elevation.

Basic loss increases by exactly 6.01 dB each time path length doubles. Ground loss predictions as far as the radio horizon are accurate within the variations expected in field strength measurements between one location and another due to random variability in soil characteristics and undulations in the terrain.

At distances 5 or 6 times greater than the radio horizon or when the total path loss exceeds 150 dB, the uncertainty in predicting field strength may be in the range +/- 15 dB. The most accurate predictions are below 2 MHz over oceanic and salt sea paths. The least accurate are at HF over steep hills, mountainous or densely populated fully developed regions. The program is useful up to 30 MHz.

Above 3.5 MHz in daylight and below 10 MHz at night, at distances greater than the radio horizon, ionospheric propagation may be as strong as or stronger than the groundwave. In multi-path conditions severe fading and distortion may occur.