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The issue I see with EZNEC is not that it doesn't recognize the radials. It's that it only appears to see them carrying transmission mode currents and that's only half the job. It is the half that reduces the high angle lobe so that is why you don't see this characteristic in your current model. The second half of the job is antenna mode currents on the cone. This is where gain above the half wave comes into play.


It is the elimination of the radiation on the lower 1/4 wave vertical that reduces the 40 degree lobe. Since you can see these results in EZNEC, we know the program is recognizing transmission mode currents taking place as we "shield" over the vertical radiator. What takes a little more digging to uncover is the fact EZNEZ does not recognize radiation from the cone and mistakes the antenna as a 180 degree radiator.


You're probably curious as to how I'm sure EZNEC is wrong here and it's easier to explain then the work I had to do to prove it to myself. If you use EZNEC to design a collinear version of this antenna, it reports peak gain using a 180 degree (or half wave) phasing section. This is correct for a half wave radiator but fails miserably in the field because the phase angles are off  by 90 degrees with this 3/4 wave. The same design shows peak gain in the field using a 90 degree phase delay, not the 180 degrees EZNEC reports.


That can only be true if a full 270 degrees (3/4 wave) of radiation had taken place prior to the 90 degree phasing section. You'll have to run the field tests yourself or just take my word on it that EZNEC is missing something on this antenna. That something appears to be the first 1/4 wave (or 90 degrees) of radiation taking place on the outside of the cone.


PS: The affects of slanting the radials down on a 3/4 wave ground plane are dramatic. It doesn't just shift impedance like on the 1/4 wave. It has a huge negative impact on the distribution of energy contained between the primary and secondary lobes. It is one of the few cases I'm aware of that significantly alters the main TOA other then height above ground.