# Height Gain

There are two approaches to prediction of radio path performance: estimation using empirical models, and numerical methods that make calculations on a path construction.

Estimation uses measurements made on a plethora of paths to build nomographs. Path loss can be read off against a small number of variables like distance.

By giving an answer based on a small number of variables, estimation does not take account of path specifics like ground height and antenna height at the stations. A correction is needed to account for antenna height.

Numerical methods are applied to a path profile and make use of constructions of the diffraction environment. Estimation gives a general answer. Numerical methods give a path-specific answer.

By defining all aspects of the path, the numerical methods approach does account for antenna height and hence no correction is needed.

This page illustrates an approach to antenna height correction usable with the page on path prediction using nomographs.

### Height correction

The notion of height gain is simple enough. Given a long-distance path (of say 300km) where the Earth’s bulge intrudes into and significantly obstructs the line of sight, path loss is estimated using a nomograph. This nomograph assumes a rough terrain and land use on top of the Earth with standard station antenna heights. The result is a standard form of path. Effectively, there’s only one variable – path distance.

If there is indeed a significant antenna height above ground at either or both stations (such as might exist at National Field Day stations), some correction is appropriate since one or both stations start to peak above the obstruction, thereby reducing the diffraction loss.

### Nomographs for path loss

Recommendation ITU-R P.526-15 gives a method using nomographs. The nomograph for horizontal polarisation over land is given below.

This illustrates a height gain of around 20dB at 144MHz (by reading off along the black line) for a station able to boast an antenna height of about 300m above surrounding terrain. This is commensurate with a high broadcast site like Ashkirk, or a contest site from an equivalent commanding hilltop with more modest antenna support.

Height gains add to the system value to give a total available loss value for the path.

### Correction for differing k

Note that because the Earth radius factor, k, modifies the ability of the elevated site to peak over the Earth bulge, the antenna gain must be corrected for variations in k. For the state for 50% of time, use the k=4/3 scale. Otherwise, for small percentages of time modify the frequency using: feff = f√k. Then use feff on the k = 1 scale. For example, for k=2.75 to emulate k exceeded for 5% of time, use a frequency of about 100MHz at 144MHz.