Skywave Trigonometry 2

Author: R.J.Edwards G4FGQ © 26th April 2006

For given values of the elevation angle and height of an ionospheric reflecting layer this program calculates the one-hop ground path and radio path distances between the transmitter and places where the radio wave returns to Earth.

Also calculated for the radio path are the "spreading loss" in decibels and the field strength in micro-volts per meter. The critical frequency, Fcrit, the frequency above which a radio wave passes right through an ionospheric layer without reflection at a 90 degree vertical angle, is also an input to the program.

The transmitting antenna is assumed to be isotropic and lays down a field covering a very wide region of the Earth's surface. By varying the elevation angle the field strength at various distances from the transmitter can be found for a transmitter power of 100 watts. F/S for other Tx powers can easily be deduced.

The reflecting layers in the ionosphere have a profound influence on the radio-wave path. There are five principal layers: D, E, F1, F2 and F. Their characteristics depend on whether or not they are under radiation by the sun, the sun-angle, the season of the year, and the 11-year sun-spot cycle.

Frequencies higher than the Critical Frequency pass right through a layer and are not reflected or refracted at vertical incidence. The angle of incidence is calculated and displayed. At incidence angles less than 90 degrees frequencies greater than Fcrit begin to be reflected. This results in layers having a Maximum Useable Frequency much greater than Fcrit which occurs with low elevation angles and very long path distances. Fcrit and layer heights are obtainable from radio observatories where daily measurements are made.

The D-Layer extends from a height of 70 to 90 kM. In sunlight it completely absorbs all frequencies from 0.1 to 2 MHz and screens all higher layers. No reflections can occur. Loss in the D-Layer extends up to 4 or 5 MHz. But below 0.1 MHz it becomes a reflector at a height of 75 kM. In darkness, the D-Layer becomes non-existent, all frequencies pass through the region with negligible loss and are reflected back to Earth from the night-time F-Layer at 300 kM.

The E-Layer is at a constant height of 115 Km in sunlight. Depending on frequency it often screens the F-layers. It is a good stable reflector for medium distance paths. At night it nearly disappears and its MUF falls to 0.5 MHz.

The F1-Layer is sometimes present in daylight at a height of 220-230 Km. It is not a stable reflector. At night it increases in height and merges with the F2 Layer to form the night-time F-Layer at heights between 280 and 320 kM.

The F2 layer in daytime is the DX workhorse. It varies in height between 350 and 450 Km. Higher in summer than in winter. Higher at the peaks of the sun spot cycle. During darkness it decreases in height and merges with the F1-Layer to become the night-time F-Layer at a height of 280 to 320 Km. The behaviour of the F2-Layer lags behind the sun by several hours.

At very low elevation angles, say less than 5 or 10 degrees, propagation is in the form of a ground wave for the first few kilometres. Radiated energy is dissipated in the ground. This is worsened by refraction in the Earth's atmosphere which causes the wave to cling to the Earth. Consequently, at very small elevation angles, there is an increasing loss in long distance signal strength. The program includes this type of loss.

Field strength depends only on transmitter power and on radio path length. As the operating frequency increases above the MUF the path is not abruptly interrupted. With increasing frequency, field strength at the end of the hop just becomes more severely attenuated. The program demonstrates this effect.

With multihop paths it is necessary to calculate each hop separately. No two hops are identical. The sun angle is different for each hop. Some hops are in sunlight and some are in darkness. So the F-Layers are at different heights. And in darkness the D and E-Layers are practically non-existent. It must be remembered, with a long multi-hop path each hop is in a different state.

From one hop to the next, provided the layers are not tilted, only the elevation angle is common to successive hops. It is layer heights which change and this affects the MUF. In a number of hops it is the lowest MUF which matters.

It is incorrect to add the dB spreading losses of individual hops together. The second hop of a pair of similar hops adds only 6 dB to the spreading loss. while a third hop adds only another 3.5 dB. A 4th hop adds 2.5 dB.

In between successive hops there is a reflection from the ground. The ground, although very large in terms of wavelengths, is not a perfect reflector and a loss is incurred. With N hops there are N-1 ground (or sea) reflections. As a rule of thumb, on average, each reflection results in a loss of about 3.5 dB.

Run this Program from the Web or Download and Run it from Your Computer
This program is self-contained and ready to use. It does not require installation. Click this link SkyTrig then click Open to run from the web or Save to save the program to your hard drive. If you save it to your hard drive, double-click the file name from Windows Explorer (Right-click Start then left-click Explore to start Windows Explorer) and it will run.

Also see: Two Hops