what is it you are hoping to achieve
OK you may all consider this a fools quest. And it may well be but it's mine.
I'm working on the design (model) of a 4 element circularly polarized electrically steered phased array antenna.
I'm aware of the article denouncing circular polarization by Tom the author of the take off angle myth article. If you desire to discuss CP start another thread and I'll submit the reasons I still want to investigate this.
Basic stats:
max gain 7.98 dbic @ 14 degrees
F/b 21 Db to 31 Db depending on angle
-3 Db horizontal beamwidth 122 degrees
-3 Db vertical beamwidth (actually height)16 degrees ( from 8 to 24 degrees)
but axial ratio is real good ( > .95 ) from about 10 through 22 degrees.
Below 10 degrees the ratio is not bad but from 24 up the ratio degrades due to a null in the horizontal gain, at 32 degrees almost all the gain is vertical.
I could eliminate the null (by mounting lower) at the cost of a Db or so. and adjust the axial ratio but of course every thing is a compromise.
I got about 12 -16 degrees of performance( from this model) where I am happy with the predicted performance may get twice that from a less aggressive gain lower mounted version but ultimately I have to decide where to aim the point (angle) where the axial ratio will be the best I can get.
And if high angles of arrival are worth listening/designing for..
The model was created before I did any mathematical attempts to find the limits of the angle of arrival so any correlation in the two are coincidence.
If you subscribe to the height is might school of thought and you believe the
Myth of TOA is applicable to all frequencies you should see what a horizontal dipoles pattern looks like at any height above about 1/2 wavelength.
Maybe the fellow in Ireland got the results he did due to nulls in his front pattern, but it looked like the propagation software and the actual contacts correlated well.
Could that fellow ever talk to the coast of France or is that in a perpetual skip zone?