This is an interesting situation, Neil. NEC4 shows that a 3-m monopole with a uniform OD of 1/2" needs about 330 µH of inductance to resonate it at 1640 kHz, when the bottom of the monopole is within a few inches of the earth and it is base-driven against a set of 8 radial wires each 6 meters long (no ground rods), buried in 5 mS/m, d.c. 13 earth.
So those numbers are very close to the NEC values for that system on 1650 kHz, which I originally modeled.
But you have had good success with your 1640 kHz antenna system when using a loading coil expected to have an inductance of about 260 µH. You have determined that r-f current and voltage are in phase at the coil feedpoint, which indicates that the antenna system is resonant.
The coil calculator linked above was loaded with the description you gave for your coil. All the entries are made in the first section at the top of the web page.
The program didn't like the use of #16 wire for these coil dimensions and 59 turns, so I dropped it back to #18 (1.024mm OD). Here is a clip of the result:

So according to this calculation, that coil would not have 260 µH of inductance, let alone the ~330 µH NEC says is needed for system resonance. But yet, your antenna system appears to be resonant with a coil of that description.
BTW, equations taken from "Reference Data for Radio Engineers" (a publication of ITT) also show that about 330 µH is needed to resonate this antenna system on 1640 kHz.
Maybe you or other readers might spot the reason for this discrepancy. So far I can't explain it, unless the coil calculator and NEC both are wrong -- which doesn't seem likely.
(Added) I just re-read your post, Neil, and see that you are using 1670 kHz, not 1640 kHz. I went back to the coil calculator and used 1670 kHz, but the results changed very little.
Thanks for looking into this. Something is apparently awry with the coil information. My coil measured L was taken with a Fluke LRC bridge which has served me very well for other measurements, always being in close agreement with calculated Ls for several coils. I would like to repeat my measurements but considering the weather this probably won't happen for some time.
Neil
While we're waiting for the weather to clear, let's look back to the start of this thread, which grew out of Rich Power's bird feeder installation.
How do the birds like it?
Yes, back to the original topic - ground rods. It's so easy to QSY in a casual conversation.
It's so easy to QSY in a casual conversation.
Could the motive for that be that persons posting such diversions don't feel competent to post on the original topic, but don't want to be left out of the on-topic discussion that follows?
You know that some of us are admittedly not "competent," to use your unflattering word, in depthful RF technology discussion.
But don't ignore, my word, that in addition to being curious about the deeper side of radio engineering, we are also concerned with a palette of topics ranging from programming to operational philosophies.
Rich, it's OK if you don't know much about birds. I find the comments about coil calcs and losses very informative even if off the topic of ground rods. Sometimes the segue is unavoidable in a casual exchange.
