# Path Loss Calculation and Profile Interpretation

## Geometry

The profile is constructed from a three dimensional terrain database extracting a terrain height at each point between the two terminals. The terrain database is at a resolution of 200 metres and hence there are about 150 terrain heights used in a path drawn North-to-South or East- to-West in a 30km path.  The number of terrain heights in a diagonal path varies with azimuth angle.  To adequately define a path it would be reasonable to use at least 10 points and hence use of this profile for short paths of under 2km is not recommended.

The profile is constructed at whatever effective Earth radius, Keff, the user needs to adequately model the path.  A value of 4/3 or 1.33 represents the geometry existing for 50% of the time in Europe.  Lower values of Keff will simulate the geometry existing for higher percentage time - a state considered useful by many microwave engineers who would typically select a value of 0.6.  Users should be mindful of this when evaluating path clearance since the Earth bulge will have greater effect in pushing terrain up into the Fresnel zone for smaller values of Keff in the case of increased atmospheric refractivity.

The red line on the profile is the fraction of first Fresnel zone ellipse or Ellipse Ratio.  If this locus of points is not obstructed by terrain, a Free Space path is said to exist at a ratio of 0.6.

Finally, it is interesting to know the most critical point on the profile at which clearance occurs.  This is identified along with the clearance distance to the nearest terrain vertically below the Fresnel ellipse.

## Path Loss

Free Space Path Loss is computed using Recommendation ITU-R P.525-2 equations 2.2.  Diffraction loss is computed using Recommendation ITU-R P.526-9 equations 4.5.  Gaseous attenuation is computed using Recommendation ITU-R P.676-5 equations 2.1.  The three loss values are reported and are added together to give the end to end path loss used in computing the received power.

## Use of the Profile

The profile is a model of the real path.  As a model it is an approximation.  The errors likely in the profile come principally from inaccuracy in the terrain data.  Since the profile is derived from a 200 metre terrain data set coming itself from SRTM data, hilltops are illustrated by the maximum height found in this area.  In this much the profile could be considered to be pessimistic.

The profile does not make use of ground clutter (vegetation and buildings).  Vegetation and buildings add to the total height at a point and hence where this exists at a sensitive point on a profile, the clearance shown and the path loss computed would be optimistic.

With these points in mind, the profile should be considered indicative rather than accurate.  Users should conduct ground surveys to establish the real heights existing at sensitive points. Sensitive points are those where a breach of the first Fresnel zone occurs or is likely given any height error.  The most sensitive points on a profile are at the terminal ends.  Here any change in height has the greatest effect.  Users should take particular care to ensure adequate clearance for the first and last 10% of the profile length.

## Further Analysis

ATDI has other terrain and clutter data available along with other topographic maps for use as backdrops including resolutions of down to 1 metre showing actual buildings and trees with aerial photography for images.  These data sets are not available for web use.  Contact us for more detailed path profile analysis including over-estuary modelling taking into account tidal changes.  Also contact us for link network planning including path modelling, frequency planning, licence applications, path surveys and coexistence studies.

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