Last Updated on November 1, 2023 by John Berry
Whether or not a path from transmitter to receiver via a meteor trail is usable depends on the meteor scatter path loss. If the path loss is too great, the received signal will be below the receiver threshold. No decode will then be possible.
The path loss depends, of course, on the characteristics of the meteor and these characteristics are highly variable. I’ve described this variability on other pages. It is possible, however, to get an idea of the median and variance of the path loss, and that’s useful in dimensioning systems.
Path loss approaches
There are two approaches to calculating the path loss: using the radar equation and using the billboard equation. Both are well established as methods in radio communications. The radar equation requires calculation of the radar cross section of the meteor trail doing the reflecting. The billboard method assumes that the energy incident on the trail sets up a coincident point source transmitter. The conversion of the incident to transmitted energy is calculate using an empirical formula.
Both methods amount to the same thing, but I shall use the billboard approach for simplicity.
I’ve outlined the arrangement below
Underdense versus overdense
The radio energy is reflected from the meteor tail. Various academics consider two cases:
- underdense trails where the electron density is low, and the energy is scattered. The reflection efficiency is low.
- overdense trails where the electron density is high, and most energy is reflected. The reflection efficiency is high.
Academics conclude that in the overdense case, the reflection coefficient is 1. For modelling, as Kaiser & Closs (1952) note, a metal cylinder can be used to represent the trail.
This case represents the base case for calculating the path loss. The reflection coefficient and the area of the effective reflector at a point on the trail are used to simulate the billboard. The calculation is shown below for a 1000km path with the reflection above the mid-point.
|Free space loss to the reflection point [a]||86.4dBi||As FSL=32.45+20logd + 20logf|
|Reflection loss of trail reflection [b]||0dB||Metal cylinder assumed|
|Billboard gain/loss at reflection [c]||9dB||As loss=20log((πd)2/|
|Free space loss from reflection point to receiver [d]||86.4dBi||As FSL=32.45+20logd + 20logf|
|Path loss||182dBi||As a + b + c+ d.|
In line with several academic works, I’ve assumed a trail width of 2 metres in the billboard gain/loss calculation.
This suggests a path loss of about 182dBi for a 2-metre-wide meteor trail. The billboard calculation suggests that the loss reduces quickly for wider trails and increases quickly for narrower trails.
This agrees well with John Worsnop G4BAO’s more precise calculations suggesting a range of loss from about 172dBi to 190dBi.
In his PhD thesis, John illustrates also how the path loss varies with the angle between the trail and transmission. He suggests about a 6dB reduction if the trail is in line with the transmission. He also notes a different loss calculation for vertical incidence transmission where the transmitter antenna is pointed directly upwards.
This value of 182dBi will be used on other pages as a guide value, recognising a variance that will exist in reality.