A.2 Spherical-Earth diffraction loss
The spherical-Earth diffraction loss not exceeded for p% time, Ldsph, is calculated as follows.
Calculate the marginal LoS distance for a smooth path:
km (A.2.1)
If d ≥ dlos calculate diffraction loss using the method in § A.3 below for adft = ap to give Ldft, and set Ldsph equal to Ldft. 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, hreq, given by:
m (A.2.3)
If h > hreq the spherical-Earth diffraction loss Ldsph is zero. No further spherical-Earth diffraction calculation is necessary.
Otherwise continue as follows:
Calculate the modified effective Earth radius, aem, which gives marginal LoS at distance d given by:
km (A.2.4)
Use the method in § A.3 for adft = aem to give Ldft.
If Ldft is negative, the spherical-Earth diffraction loss Ldsph 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 Ldft for a given value of effective Earth radius adft. The value of adft to use is determined in § A.2.
Set 
and 
where 
and 
appear in Table 2.3.1. Calculate Ldft using equations (A.3.2) to (A.3.8) and call the result Ldftland.
Set 
and 
where 
and 
appear in Table 2.3.1.
Calculate Ldft using equations (A.3.2) to (A.3.8) and call the result Ldftsea.
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 KH or KV according to polarization, see Tpol 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)