Continue for both cases

Calculate the horizon elevation angles limited such that they are positive.

                mrad (3.7.11a)

                mrad (3.7.11b)

3.8 Effective heights and path roughness parameter

The effective transmitter and receiver heights above terrain are calculated relative to a smooth surface fitted to the profile.

Calculate the initial provisional values for the heights of the smooth surface at the transmitter and receiver ends of the path, as follows:

(3.8.1)

(3.8.2)

                masl (3.8.3a)

                masl (3.8.3b)

If , re-evaluate h_stip using:

                masl (3.8.4a)

If , re-evaluate h_srip using:

                masl (3.8.4b)

The slope of the least-squares regression fit is given by m:

                m/km (3.8.5)

The effective heights of the transmitter and receiver antennas above the smooth surface are now given by:

                m (3.8.6a)

                m (3.8.6b)

Calculate the path roughness parameter given by:

                m (3.8.7)

where the profile index i takes all values from i_lt to i_lr inclusive. The path roughness parameter, h_m, is used in Appendix D.

Further calculations involving the smooth surface are now required for the obstruction gain correction described in Appendix A.

Find the highest obstruction height above the straight-line path from transmitter to receiver h_obs, and the horizon elevation angles α_obt, α_obr, all based on flat-Earth geometry, according to:

                m (3.8.8a)

                mrad (3.8.8b)

                mrad (3.8.8c)

where:

                m (3.8.8d)

and the profile index i takes values from 2 to (n – 1).

Calculate provisional values for the heights of the smooth surface at the transmitter and receiver ends of the path:

If h_obs is less than or equal to zero, then:

                masl (3.8.9a)

                masl (3.8.9b)

otherwise:

                masl (3.8.9c)

                masl (3.8.9d)

where:

(3.8.9e)

(3.8.9f)

Calculate the final values for the heights of the smooth surface at the transmitter and receiver ends of the path:

If h_st is greater than h₁ then:

                masl (3.8.10a)

If h_sr is greater than h_n then:

                masl (3.8.10b)

Calculate the effective antenna heights for the spherical-earth and the smooth-profile version of the Bullington model (described in §§ A.2 and A.5, respectively) given by:

                masl (3.8.11a)

                masl (3.8.11b)

3.9 Tropospheric-scatter path segments

For the tropospheric-scatter model described in Appendix E, calculate the horizontal path lengths from transmitter to common volume and common volume to receiver:

                km (3.9.1a)

Limit d_tcv such that 0 ≤ d_tcv ≤ d:

                km (3.9.1b)

where d, _e, _tpos, and _rpos all appear in Table 3.1.

Calculate the longitude and latitude of the common volume, _cve and _cvn, from the transmitter and receiver longitudes and latitudes, as given in Table 2.2.1, using the great circle path method of Appendix H by setting d_pnt = d_tcv in equation (H.3.1).

Calculate the height of the troposcatter common volume given by:

                masl (3.9.2)

Calculate the longitude and latitude of the mid-points of the path segments from transmitter to common volume and from receiver to common volume, _tcve, _tcvn, and _rcve, _rcvn. These can be obtained using the great circle path method of Appendix H by setting d_pnt = 0.5 d_tcv and d_pnt = d − 0.5 d_rcv in equation (H.3.1), respectively.