Hi again.
My follow up answer may sound lazy to you (it is) but if you are interested in antennas, you need to buy the ARRL Antenna Book. This truly is a comprehensive volume of all things antennas, including grounding. Chapter 3 (of my 24th edition) is all about grounding.
Now, before picking out the points that I think are most important, let me begin with my tired old speech about complexity. Amateur radio is an exercise in compromise. Anything we do has so many variables. Whether it be grounding, transmission, lines, or antenna design, it's never as simple as a single variable. I could also add that modern day antennas, paired with modern day feedlines and modern day transceivers allow us to overcome many of the shortcomings of a mediocre installation. Obviously, a bad installation is a bad installation, but if an antenna is properly designed, relatively well tuned, and installed not too close to a building or to man-made interference, then it will more than likely operate acceptably well.
Now back to the question about length. First of all, good grounding assumes a flat ground. Does it make a difference considering what I just said above? Actually it does. Many have tested what an inclined plane does to a signal and it's very noticeable. As for the number and length of radials, this is where it gets super duper complex (or not). The complex version is too long to type here but suffice it to say that because of ground conductivity, because of wire thickness, because of height above ground (or below) that the number and length of radials is incalculably variable.
The conventional wisdom among amateurs is definitely that the radial should be the length of the height of the antenna. Another bit of conventional wisdom is that the shorter the antenna, the more wires you need. This actually makes life simpler because the, as you can imagine, cutting dozens of wires that are the length of a half wave 80m antenna will be expensive and a PITA.
A third bit of conventional wisdom, and btw, all of these 'conventional wisdoms' are backed by actual numbers and years of trial and error. So, the third bit is that given the choice between length and quantity of radials, length is better.
A very important element in radial design is to be equal! If you have something in the way on one side, forget it... You're better off having all the radials shorter but the same length.
As to the number of radials, based on a 1937 study, broadcast towers were deemed effective when they had 120 radials!!!!!! Not a typo. My advice to all amateurs has been the following. I like the number 16. I can calculate my way higher or lower, but 16 has always worked for me, both in practice and mathematically. But if you want absolute precision, I will take the time to calculate the exact/approximate number and length 😉
Not sure if this has been helpful or useless...
until