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Figure 12.22. Geometric representation of a one-hop HF path where deff is the distance APB.

above the earth's surface at midpoint. The effective distance deff can be calculated:

deff s 2^8.115 X 107 q 12,740h\ q h\2 - cos J X (8.115 X 107 q 12,740h^)

Equation (12.9) assumes ri, the radius of the earth in Figure 12.22, to be 6370 km; a is the great circle arc from A to B, and h\ is the virtual reflection height. We can calculate a from the great circle equation:

where a = angle of the great circle arc (see Figure 12.22) A = latitude of station A B = latitude of station B A L = difference in longitude between stations A and B

We can also derive deff from Figure 12.23 where h is the reflection point height above the earth's surface. The height of the reflection point h can be derived from Figure 12.27.

Figure 12.23. Effective distance deff when given the great circle distance and reflection height h. (From Ref. 33.)

12.10.2.2 D-Layer Absorption Losses. D-layer absorption is a daytime phenomenon. The D-layer disappears at night. D-layer absorption varies with the zenith angle of the sun, the sunspot number, the season, and the operating frequency. In fact, it varies as the inverse of the square of the operating frequency. This latter fact is one reason we are driven to use higher frequencies for skywave links, to reduce D-layer absorption.

To calculate D-layer absorption on a particular skywave path, we first compute the absorption index I:

where R is the sunspot number and x is the solar zenith angle of the sun. If X is greater than 100°, it is nighttime and we can neglect D-layer absorption.

From Ref. 5, we calculate the solar zenith angle with the following formula:

geographical latitude solar declination the local hour angle of the sun measured westward from apparent noon, which is mean noon corrected for the equation of time and the standard time used at the location of interest

Tables of hourly values of cos x from sunrise to sunset for the 15th day of each month for most of the ionosphere vertical incidence sounding stations are given in the URSI Ionosphere Manual (Ref. 33, p. 19). From Ref. 34, the hour angle of the sun, h, is calculated:

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