Calculator to Estimate Mountain-Bounce Radio Transmission Loss

(to Predict Received Signal Power)

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 predicts the received signal power for particular stations and geometry. The model used is very close to the "bi-static radar" range equation. One of the inputs is the experimentally derived "Scattering Efficiency," expressed in dB. There is a separate calculator. to aid in getting efficiency numbers for different situations.

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.

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

Mountain Charicteristic - Enter estimated Scattering Efficiency here. If you are lacking specific data, here are a few rules-of-thumb:

Mountain Data Input
Scattering Efficiency, dB

Station 2 (receiving station) Parameters

Station 2 Data Input
Distance to Mountain
Visible Mountain Height
Mountain Top Angle

Path Loss Prediction - The received power is in dBm. To put this into perspective, rough rules of thumb 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. If one only wants the estimate of path loss, take the Station 1 transmitter power in dBm above, and subtract the received power here.

Calculated Receive Signal Power
Received Power, dBm Calculated  

The "Reset" test case should calculate --120.0 dBm.

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