# Positions vs distance

I was wondering why the number of reported positions is almost the same for zone 1 (0-80km), zone 2 (80-160km) and zone 3 (160-240km). I expected the number to drop as when the distance increases. This might be low hanging fruit, but I was surprised to learn that these diameters are probably not random chosen. The area of each zone relates to the first with a factor 1,3,5,7 or 9. That kind of explains why the number of positions at greater distances could be quite high.

The area ratio is something of a coincidence, it is just a direct result of the range ratio 1:2:3:4:5:

``````

area N = pi * radiusN ^ 2 - pi * radius(N-1) ^ 2
= pi * (N^2 * radius1 ^ 2 - (N-1)^2 * radius1 ^ 2)
= pi * radius1 ^ 2 * (N^2 - (N-1)^2)
= area(1) * (2N - 1)

``````

Offhand, I would guess that the effect is something like:

• you can see messages from every aircraft in line of sight quite reliably, up to a maximum range determined by the gain of your system, then there is a quite sharp cutoff
• the volume of airspace that is visible is approximately inversely proportional to distance, which cancels out with the ring area being approximately proportional to distance

The numbers are “rounder” if you switch to miles.
As for the density of flights, it is depending on the location of the antenna to the local main flight paths. Local airports traffic will be seen also different.

Airplanes are not equally found in the sky, the follow specific lanes, it’s not an entropic system.

The distribution of aircraft is clumped.