I have some historical data on radio stations, but unfortunately, the dataset only has these variables:
the power of the transmitter, in watts
the coordinates of the radio tower
Unfortunately, I don't have any data on the characteristics of the antenna(s) or the radio towers themselves, e.g. their height. Anecdotally, the frequencies of these stations are from 500 to 1500 kilocycles, which I believe are AM frequencies.
I asked a similar question on the physics.SE and was told that, with an example of a 500 W transmitter, I can very roughly estimate the strength at a distance of, say, 10 km, as
At a distance of $10km$, that power is uniformly distributed over a sphere of radius $10km$. In other words, the power per $m^2$ will be
$\frac{500}{4 \pi r^2}$ in units of $\frac{watt}{m^2}$.
In this example, this gives me approximately $4 \times 10^{-7} \frac{\text{watts}}{m^2}$, or -33.98 dBm per square meter.
With that number in hand, is there anything I can say about a receiver's ability to pick up that signal? As in, a standard household radio receiver in the 1920s could, on average, audibly receive signals down to strength -25 dbm, so it probably wouldn't be able to pick up this signal?
Or is the more appropriate way to convert this power into $V/m$ and use an approximation of the audible area like in this article?
(Yes, I know this is an overly simplistic approximation; I'm trying to do the best I can with the extremely limited data that I have. It was recommended that I ask here, so any information is most welcome!)