Just a little empirical work. Not much out there in the literature. A quarterwave monopole over a halfwave ground plane has a phase center around 25% up the whip.
I had just started working on phase center, still not get clue from where to start, i am working on patch and found only one paper from Dr Jackson group. In this field and work is carried out by one phd student L Basillio, but i am not able to get the paper too.
Can you help me out in start with the initial calculation.
Sorry, I am not an antenna guy. Someone once told me that you could use the 4NEC2 program to calculate phase centers, but I have not tried it.
I suspect you could start with a paper like this one, and solve the efield equations for phase angle as you varied azimuth/elevation, and you would see the phase center that way.