Sorry to be late in my added response to this thread.
DB, below are two model overlays I posted for my New V4K vs. Antenna Specialists version of the Sigma 4. Both models are set to the specs I have based on my real S4 antenna and the NV4K specs are as posted by Bob85 some time back on this forum. Early in this thread I posted my model of the Vector 4k with and without radials using the mount noted in Bob's specs. You are correct I placed the radials at the bottom of the V4K mount noted as 13.75" inches long and below the hub.
When you posted above that you placed your radials on the Vector at or close to the base of the hub, I had the thought this difference might make a noticeable difference, so I modified my radials as close to the hub as I could get. 1" inch will work with a slight difference to be noted, but I decided to make the mount 4" inches below the hub instead. Again, I noticed only a slight difference in the results...with no difference in gain/angle but a small difference in the match.
I read the whole thread again and saw where Bob mentioned Henry's published report on "The Avanti Sigma 4.
http://cb-antennas.com/?page_id=780
This gave me the idea that maybe the S4 and the NV4K, having different dimensions primarily in the cones radial length, might also account for the difference that Bob mentions regarding Henry's information on page 41, "Room for Improvement?"
So, I modified my models and posted the overlays below.
If my model overlays are close, and it is questionable for sure, then maybe Henry's results were accurate but only for the Sigma 4 with radials added.
My models do not include the gamma match, albeit the matches are fair and suggest the antennas are safe for radio operations. That said DB, I cannot add more to your ideas about the gamma match effects that you included in your models.
All my models show Average Gain results in Free Space no worse than 0.998 - 1.002.
You will notice in the overlays that the S4 with 3 horizontal 89" inch radials close to the hub shows the best gain of 5.58 dbi at 9* degrees TOA. The V4K without horizontal radials added is a close second with its gain of 5.44 dbi at 8* degree TOA. The angle difference maybe worth noting however.
I tuned the S4 horizontal radials I added to the best length for maximum gain, but I forgot to do the same on the NV4K. I will follow up if such a fix for the NV4K makes a notable difference.
As you note DB, there are just too many difference in the dimensions to be sure about our trying to compare these results. I can only guess that maybe the added length of the cone elements is possibly making some difference.
I used a Sigma 4 with 3 x 90.5" inch elements in the cone and then added 3 x 89" inch horizontal radials 4" inches below the hub for my modified model of the S4.
I also added 4 x 108" inch horizontal radials 4" inches below the hub on my NV4K with 4 x 107" inch elements in the cone. I forgot to check the radial lengths for best gain on the Vector model however.
Well Bob, my Sigma 4 model with 3 x 89" inch horizontal radials added...shows the maximum gain for this group. My NV4K with 4 x 9' foot horizontal radials added came in last among the group. My S4 model with 3 horizontal radials added shows the best far field results. If this is close to accurate then maybe this is indicative of Henry's surface wave model results...and maybe DB's model of the Vector is less effected by adding horizontal radials like I think he has suggested.
The use of the (*) beside the models in the PDF file below is the active model. This shows the gain and angle results to the right of the page below the pattern.
I can't add any more ideas in response to your question Bob.
