Maximum Usable Angle
By Ken Larson, KJ6RZ
We are all relatively familiar with the term maximum usable frequency since it often appears as a question on amateur radio license exams. Maximum usable angle is the other half of the maximum usable frequency equation. Maximum usable frequency is important for determining the best HF frequency to use in communicating between two locations, for example between Los Angles and Denver. The maximum usable frequency depends in part on the distance between to two locations. Thus the maximum usable frequency for communicating between Los Angles and San Diego will be different from that to communicate between Los Angles and Denver. In the past, maximum usable frequency was very important to professional communicators who were interested in operating full time HF communication circuits between specific locations, for example from Guam to North West Cape Australia. Today commercial HF circuits are probably less important than in the past because of the wide availability of communication satellites. Maximum usable frequency is still important to amateur radio operators interested in scheduling contacts with distant friends, communicating with a specific country, and in operating regional ARES/RACES HF emergency communication circuits. For general amateur radio work, however, maximum usable angle is probably more important than maximum usable frequency. Maximum usable angle focuses on band availability, the types of antennas needed to take advantage of band openings, and the skip distances that can be expected. To understand maximum usable angle, and it implications, we must start with the maximum usable frequency equation. The maximum usable frequency for communicating between two locations is: Fm = Fo / (sin Ae) In this equation Fo is the critical frequency for the F layer of the Ionosphere. Fo is the highest frequency signal that can be transmitted directly upward, reflected by the Ionosphere, and return to Earth. The critical frequency Fo varies throughout the day, seasonally, and in accordance with the 11 year solar sunspot cycle. Fo is at its lowest value of the day, typically around 4 MHz, in the morning just before sunrise. It rises quickly during the morning reaching a maximum of around 9 MHz at noon, and then decreases throughout the afternoon and night reaching a minimum again the following morning. At noon during a solar sunspot maximum, Fo may be as high as 14 MHz. During a sunspot minimum, Fo may be 3 MHz or less prior to sunrise and reach only 5 MHz at mid day. The angle Ae is the elevation angle, with respect to horizontal ground, of the transmitted signal as it leaves the antenna. (Actually, the vertical radiation pattern for an antenna can be quite complicated, so the angle Ae referred to here is the angle of the main lobe in the vertical radiation pattern.) For the maximum usable frequency equation, Ae is the angle at which a signal must be transmitted to reach the desired location. As shown in Figure 1, a small or low elevation angle Aea causes the transmitted signal to travel a long distance, refracting in the Ionosphere and returning to Earth at location A. The maximum usable frequency for this elevation angle is Fma. Any frequency less than Fma, transmitted at an angle of Ae will also be refracted by the Ionosphere and return to Earth. However, frequencies greater than Fma will pass through the Ionosphere and be lost to outer space. If the elevation angle is increase to Aeb , the transmitted signal will travel a shorter distance returning to Earth at point B. The maximum usable frequency fMB will also be less than Fma. If the elevation angle is increased to Aet = 90 degrees, the transmitted signal will travel straight up, be reflected by the Ionosphere, and travel straight down again to the transmitting location T. At an angle Aet = 90 degrees, the maximum usable frequency fMT is equal to the critical frequency Fo. The main lobe elevation angle depends on the configuration of the transmitting antenna. Vertical antennas have low elevation angles while horizontal dipoles and yagi antennas have low to high elevation angles depending on their height (measured in wavelengths) above ground, as shown in the table below. The numbers in parentheses are the angles for the -3db points on the antenna's main lobe.
|
Table 1 |
Antennas | Elevation Angle in Degrees |
---|---|
Vertical | |
1/4 wavelength long | 28 (15 - 40) |
3/8 wavelength long | 23 (12 - 35) |
1/2 wavelength long | 18 (09 - 25) |
5/8 wavelength long | 12 (07 - 18) |
Hortizontal Dipole | |
1/8 wavelength long above ground | 90 (55 for lower 3db point) |
1/4 wavelength long above ground | 60 (38 - 82) |
1/2 wavelength long above ground | 30 (18 - 40) |
3/4 wavelength long above ground | 21 (14 - 28) |
One wavelength long above ground | 17 (09 - 19) |
Hortizontal Yagi | |
1/4 wavelength long above ground | 43 (32 - 54) |
1/2 wavelength long above ground | 30 (18 - 38) |
3/4 wavelength long above ground | 21 (13 - 28) |
One wavelength long above ground | 17 (09 - 18) |