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# Terms Used in the Study of Sky Wave Propagation

As the wave is refracted, it is bent down gradually rather than sharply. However, below the ionised layer, the incident and refracted rays follow paths that are exactly the same as they would have been if reflection had taken place from a surface located at a greater height, called the virtual height of this layer. If the virtual height of a layer is known, it is then quite simple to calculate the angle of incidence required for the wave to return to ground at a selected spot.

Sub Topics

## Critical Frequency (fc)

The critical frequency (fc) for a given layer is the highest frequency that will be returned down to Earth by that layer after having been beamed straight up at it. It is important to realise that there is such a maximum, and it is also necessary to know its value under a given set of conditions. This value changes with these conditions.

A wave will be bent downward provided that the rate of change of ionisation density is sufficient.

Actual and virtual heights of an ionised layer

The maximum usable frequency, or MUF, is also a limiting frequency, but this time for some specific angle of incidence other than the normal. In fact, if the angle of incidence is q, it follows that

This is the so-called secant law, and it is very useful in making preliminary calculations for a specific MUF. Strictly speaking, it applies only to a flat Earth and a flat reflecting layer.

## Skip Distance

The skip distance is the shortest distance from a transmitter, measured along the surface of the Earth, at which a sky wave of fixed frequency (more than fc) will be returned to Earth. One expects there to be a maximum distance, as limited by the curvature of the Earth, but nevertheless a definite minimum also exists for any fixed transmitting frequency. The reason for this becomes apparent if the behavior of a sky wave is considered with the aid of a sketch [below figure].

When the angle of incidence is made quite large, as for ray 1 of the below figure, the sky wave returns to ground at a long distance from the transmitter. As this angle is slowly reduced, naturally the wave returns closer and closer to the transmitter, as shown by rays 2 and 3. If the angle of incidence is now made significantly less than that of ray 3, the ray will be too close to the normal to be returned to Earth. It may be bent noticeably, as for ray 4, or only slightly, as for ray 5. In either case the bending will be insufficient to return the wave, unless the frequency being used for communication is less than the critical frequency {which is most unlikely}; in that case everything is returned to Earth. Finally, if the angle of incidence is only just smaller than that of ray 3, the wave may be returned, but at a distance farther than the return point of ray 3; a ray such as this ray 6 of below figure. This upper ray is bent back very gradually, because ion density is changing very slowly at this angle. It thus returns to Earth at a considerable distance from the transmitter and is weakened by its passage.

Effects of ionosphere on rays of varying incidence

Ray 3 is incident at an angle, which results in its being returned as close to the transmitter as a wave of this frequency can be. Accordingly, the distance is the skip distance. It thus, follows that any higher frequency beamed up at the angle of ray 3 will not be returned to ground. It is seen that the frequency, which makes a given distance correspond to the skip distance, is the MUF for that pair of points.

At the skip distance, only the normal or lower ray can reach the destination, whereas at greater distances, the upper ray can be received as well, causing interference. This is a reason why frequencies not much below the MUF are used for transmission. Another reason is the lack of directionality of high-frequency antennas. If the frequency used is low enough, it is possible to receive lower rays by two different paths after either one or two hops, as shown in the below figure. The result of this is interference once again.

Multipath sky-wave propagation

## Transmission path

The transmission path is limited by the skip distance at one end and the curvature of the Earth at the other. The longest single-hop distance is obtained when the ray is transmitted tangentially to the surface of the Earth, as shown in below figure. For the F2 layer, this corresponds to a maximum practical distance of about 4000 km. Since the semi-circumference of the Earth is just over 20,000 km, multiple-hop paths are often required. The below figure shows such a situation. No unusual problems arise with multi hop north-south paths. However, care must be taken when planning long east-west paths to realize that although it is day "here," it is night "there," if "there" happens to be on the other side of the terminator. The result of not taking this into account is shown in the below figure. A path calculated on the basis of a constant height of the F2 layer will, if it crosses the terminator, undershoot and miss the receiving area as shown-the F layer over the target is lower than the F2 layer over the transmitter.