A.2 Spherical-Earth diffraction loss

The spherical-Earth diffraction loss not exceeded for p% time, L_dsph, is calculated as follows.

Calculate the marginal LoS distance for a smooth path:

km (A.2.1)

If d ≥ d_los calculate diffraction loss using the method in § A.3 below for a_dft = a_p to give L_dft, and set L_dsph equal to L_dft. No further spherical-Earth diffraction calculation is necessary.

Otherwise continue as follows:

Calculate the smallest clearance height between the curved-Earth path and the ray between the antennas, h, given by:

m (A.2.2)

where:

km (A.2.2a)

km (A.2.2b)

(A.2.2c)

where the arccos function returns an angle in radians.

(A.2.2d)

(A.2.2e)

Calculate the required clearance for zero diffraction loss, h_req, given by:

m (A.2.3)

If h > h_req the spherical-Earth diffraction loss L_dsph is zero. No further spherical-Earth diffraction calculation is necessary.

Otherwise continue as follows:

Calculate the modified effective Earth radius, a_em, which gives marginal LoS at distance d given by:

km (A.2.4)

Use the method in § A.3 for a_dft = a_em to give L_dft.

If L_dft is negative, the spherical-Earth diffraction loss L_dsph is zero, and no further spherical-Earth diffraction calculation is necessary.

Otherwise continue as follows:

Calculate the spherical-Earth diffraction loss by interpolation:

(A.2.5)

A.3 First-term spherical-Earth diffraction loss

This subsection gives the method for calculating spherical-Earth diffraction using only the first term of the residue series. It forms part of the overall diffraction method described in § A.2 above to give the first-term diffraction loss L_dft for a given value of effective Earth radius a_dft. The value of a_dft to use is determined in § A.2.

Set and where and appear in Table 2.3.1. Calculate L_dft using equations (A.3.2) to (A.3.8) and call the result L_dftland.

Set and where and appear in Table 2.3.1.

Calculate L_dft using equations (A.3.2) to (A.3.8) and call the result L_dftsea.

First-term spherical diffraction loss is now given by:

(A.3.1)

where w is the fraction of the path over sea, and appears in Table 3.1.

Start of calculation to be performed twice

Normalized factor for surface admittance for horizontal and vertical polarization:

(horizontal) (A.3.2a)

and:

(vertical) (A.3.2b)

Calculate the Earth ground/polarization parameter:

(A.3.3)

where K is K_H or K_V according to polarization, see T_pol in Table 2.2.1

Normalized distance:

(A.3.4)

Normalized transmitter and receiver heights:

(A.3.5a)

(A.3.5b)

Calculate the distance term given by:

(A.3.6)

Define a function of normalized height given by:

(A.3.7)

where:

(A.3.7a)

Limit G(Y) such that

The first-term spherical-Earth diffraction loss is now given by:

dB (A.3.8)