I am interested in your models above, and it seems your 1/2 wave is the best on the overlay. I didn't see the 1/4 in there.
I wasn't suggesting gain is tied to capture area, I said I think of capture area in terms of the overall sizes of the antennas.
I'll try to clarify.
Gain in the case of the 1/2 wave and the 1/4 GP are exactly opposite to the overall capture area.
1/2 = more gain with less capture area
1/4 GP = less gain with more capture area
A 1/4 GP has 9' of upward radiator, and 3 or 4 x 9' of downward radiators - more overall area of approx 18 linear feet from top to bottom.
A 1/2 wave has 18' linear feet too, but less physical area. It relies on the way it is made to produce advantages electrically over the 1/4 GP.
Even if one does not accept that the 1/4 GP with its 4 radials has more CA than the 1/2 wave, it nevertheless will show that equal CA doesn't guarantee equal gain.
That is why we are basically in agreement on the CA thing.
And, that is why I see and experience the potential of the AP.
It is not a matter of physical size/length except as those things are a part of what produces definite electrical advantages that generate more gain.
I wish I had left the part about capture area out of my original repost. It was a comment made within a given context that is lacking in this thread.
It may have value if it doesn't lead to a misunderstanding of why I think any of my antennas work as well or ,so poorly, as they do.
The electrical response to the physical attributes of an antenna is what produces gain.