(12) where: i : angle of incidence at height hr = 110 km R0 : radius of the Earth, 6 371 km F : elevation for the F2-layer mode (determined from equation (13)). PART 2 Median sky-wave field strength 5 Median sky-wave field strength The predicted strength is the monthly median over all days of the month. The prediction procedure is in three parts, dependent on the path length. For path distances less than 7 000 km predictions of median sky-wave field strength are made using only the method given in § 5.2. For path distances greater than 9 000 km median sky-wave field strengths are made using only the method given in § 5.3. For path distances between 7 000 and 9 000 km both methods are used and the results are interpolated by the method described in § 5.4. 5.1 Elevation angle The elevation angle which applies for all frequencies, including those above the basic MUF, is given by: (13) d : hop length of an n-hop mode given by d = D/n hr : equivalent plane-mirror reflection height for E modes hr = 110 km for F2 modes hr is taken as a function of time, location and hop length. The mirror reflection height for F2 modes, hr, is calculated as follows, where: x = foF2/foE and with: and y = x or 1.8, whichever is the larger. a) For x > 3.33 and xr = f / foF2 1, f is the wave frequency: hr = h or 800 km, whichever is the smaller (14) where: h = A1 + B1 2.4–a for B1 and a 0 = A1 + B1 otherwise with:
The value fM is determined separately for the two control points from the product of the K-factor and the basic MUF. The lower value is taken as the operational MUF for the whole path. fM = K · fBM MHz (31) The K-factor is used to calculate the operational MUF fM from the basic MUF fBM: (32) where: fBM,noon : value of fBM for a time corresponding to local noon fBM,min : lowest value of fBM which occurs during 24 hours. W, X and Y are in Table 3. The azimuth angle of the great-circle path is determined at the centre of the whole path; this angle is used to linearly interpolate the angle between the East-West and NorthSouth values. TABLE 3 Values of W, X and Y used for the determination of the correction factor K W X Y East-West 0.1 1.2 0.6 0.2 0.2 0.4 5.3.2 Determination of the fL The LUF is strongly influenced by non-deviative absorption. HF waves are absorbed by penetrating the D-Layer. For the determination of the LUF, the path is divided into nL equal hops dL in length (none longer than 3 000 km). The penetration points are determined by assuming a fixed reflection height of 300 km and a penetration height of 90 km (two penetration points per hop). The fL is calculated by equation (33): MHz (33) m: number of penetration points 2nL R12: sun spot number which does not saturate for high values and can exceed 160 : zenith angle which can be calculated by the following equation: (34) δ: declination (radians) φm: geographical latitude of the mth penetration point (radians) hour angle (radians). The solar declination, δ, can be approximated by the subsolar latitude for the middle of the month (sx) from Table 4:
where: For the succeeding three hours (n = 1, 2 and 3), fL is calculated by: (38) The newly recalculated fL values replace the initial fL values only if they are larger. Once all fL values in a 24-hour period are calculated, the current hour fL value is selected and the fL calculation is complete. 5.3.3 Estimation of the field strength Etl The resultant median field strength Etl is given by: – 30.0 + Pt + Gtl + Gap – Ly dB(1 V/m) (39) where E0 is the free-space field strength for 3 MW e.i.r.p. In this case: E0 = 139.6 – 20 log p dB(1 V/m) (40) where: p is calculated using equations (19) and (13) with hr = 300 km Gtl: largest value of transmitting antenna gain at the required azimuth in the elevation range 0° to 8° (dB) Gap: increase in field strength due to focusing at long distances given as: dB (41) As Gap from the above formula tends to infinity when D is a multiple of R0, it is limited to the value of 15 dB. Ly: a term similar in concept to Lz. The present recommended value is –0.14 dB NOTE 1 – It should be noted that the value of Ly is dependent on the elements of the prediction method, so that any changes in those elements should be accompanied by revision of the Ly value fH: mean of the values of electron gyrofrequency determined at both control points fM: MUF (see § 5.3.1) (see § 5.3.2). 5.4 Paths between 7 000 and 9 000 km In this distance range the median sky-wave field strength Eti is determined by interpolation between values Es and El. Es is the root-sum-squared field strength given by equation (28) and El refers to a composite mode as given by equation (39). dB(1 V/m) (42) with: where: and