Skywave Trigonometry

For given one-hop ground path distance and height of reflecting layer this program calculates radio path distances and the radio-path elevation angle.

The remainder of the program assists with appreciation of how radio waves propagate via the ionosphere and how losses are crudely proportioned. Greatest loss occurs due to dispersion (spreading out) of waves in space. Then come ground absorption and reflection losses which increase rapidly for small elevation angles. Under calm conditions only a moderate loss occurs due to absorption in the ionosphere. Under disturbed conditions ionospheric loss is subject to great variability. The program crudely assumes "average" conditions.

For simplicity MUF, Maximum Useable Frequency, is disregarded. This depends on the angle of incidence between the radio path and the reflecting layer. It is influenced by the Sun's elevation angle, on seasonal variations, etc.

It frequently occurs that two paths are simultaneously available between transmitter and receivers each path using a different number of hops. This causes the resulting signal to fade, perhaps flutter and become distorted - multi-path distortion.

• Dispersion, spreading loss between transmitter and receiver assumes both antennas are dipoles.
• Receiver input volts assumes antenna and the 50-ohm receiver are impedance-matched.
• Transmitter power output = 100 watts CW
• Antenna radiating efficiency = 100%
• Receiver S-meter is calibrated according to the de-facto standard.
• The midpoint of a hop decides whether a hop is in daylight or darkness.
• Layer heights are assumed to be the same for both hops.
• Remember: Signal strength can vary by 15 dB or more depending on conditions.

The Following Notes are not Directly Connected with the Program, but may be of Interest.
Fcrit, critical frequency is the frequency at which the wave penetrates a layer at vertical incidence without reflection. As elevation angle decreases so does the angle of incidence - and the MUF increases according to the relationship MUF = Fcrit/Sin(Angle-of-incidence). So highest MUFs occur at low angles and at long distances. If frequency increases above MUF propagation loss rapidly increases.

Lowest useful frequency occurs when a lower-height reflecting layer intervenes between ground and a desired reflecting layer. The D-layer, at 70 km, rapidly absorbs radio waves in daylight below about 3-4 MHz to screen all other layers. So the amateur 160 meter band is of no use in daylight except on groundwaves up about 80-100 miles. Frequencies above 5 MHz are unaffected by the D-layer.

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 TwoHops 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: Sky Trig