Calculator to Find Mountain-Bounce Radio Scattering Efficiency from Measured Data

Bob Larkin W7PUA

Purpose - This calculator applies to radio receiving systems operating at frequencies above about 100 MHz. Mountain bouncing utilizes a high structure that is line-of-sight from two radio systems. This, of course need not be a real mountain, but could be a cliff or a water tower. Both stations point directive antennas at the mountain, some portion of the radio energy hits the mountain and is scattered towards the second station. At the second station, a portion of the scattered energy is captured by the receiving antenna.

This calculator is used after an experiment is performed that measured the transmission loss on a bounce path. This is done by measuring the transmitted power and the received power. This calculator combines the measurements with antenna performance and the path geometry to calculate the Scattering Efficiency. This is a measure of the fraction of the power incident on the mountain that is scattered towards the receiving station. It is expressed in negative dB. Efficiency knowledge gained from these measurements allows prediction of the received power on new paths, using a separate calculator.

Enter data to the boxes and click on the "Calculate" button. The "Reset" button loads test case data. The "Detail" button will show additional information related to the problem.

The model used is very close to that of the "bi-static radar" range equation. In the following, station 1 is the transmitting station and station 2 is the receiving station. The distances are from the stations to the mountain. The mountain height is only that portion that is visible from each station, NOT the total height. The mountain area is modelled as a triangle with the total included angle at the top as entered. Antenna sizes are physical diameters (for parabolic dishes or horns). An aperture area efficiency of 50% is assumed.

Select units:

Meters and km
Feet and miles

A measure of gain is needed for both stations. Depending on the type of antenna, it may be most convenient to use the physical aperture (eg, for parabolic dish and horn types), or to use the power gain (for Yagis). The latter gain can be referenced to either an isotropic radiator (dBi), or to a half-wave dipole (dBd).

Physical aperture diameter
Gain over an isotropic radiator, dBi
Gain over a dipole, dBd

Station 1 (transmitting station) Parameters - Transmitter power is in dBm (dB relative to a milliWatt, i.e., 30 dBm is 1 Watt).

Station 1 Data Input
Frequency, MHz
Transmit Power, dBm
Distance to Mountain
Visible Mountain Height
Mountain Top Angle

Station 2 (receiving station) Parameters - The received power is in dBm. If no measurement is available, some rules of thumb that might help are (for ordinary receivers): CW copy begins at -145 to -150 dBm, SSB copy begins at -135 to -140 dBm and NBFM copy begins at -125 to -130 dBm.

Station 2 Data Input
Received Power, dBm
Distance to Mountain
Visible Mountain Height
Mountain Top Angle

Scattering Efficiency - If the power intercepted by the mountain was scattered equally in all directions, some part corresponding to it's capture area would be received at station 2. That corresponds to 100% scattering Efficiency, or 0 dB. It is concievable that the power could be focussed on the receiving station. For that case the efficiency could be over 100% or positive dB. In reality, much of the power is absorbed and in some cases greater amounts of power is scattered in directions away from the receiving station. All of this reduces the received signal level as indicated by the observed Scattering Efficiency.

Calculated Scattering Efficiency
Scattering Efficiency, dB Calculated  

The "Reset" test case should calculate -23.5 dB.

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