@Ash Yes of course, absolutely I can use the big equation with ballast impedance to determine PF, that is what I did to determine the average PF values across technologies. These averages are good enough to get ballast characteristics for most more common lamps.
But for other rarer lamps (short arc LPS, linear neon, super high pressure lamps), these averaged technology values are probably far from what the particular lamp actually is. I am sure it would not be wise of me to assume that my NA-1 has the same PF as an average SOX or SOX-E lamp, even though both are under the LPS category they surely are very different. And I am sure linear neon has a PF that is different from fluorescent even though they are physically similar. I don't have ballast specs for these less common types of lamps.
So naturally the need arises to get the power factor of a lamp which you don't have the ballast specs for, so you can use that PF to calculate the ballast specs. Let's use a 160W NE/H for example. I know that a 160W NE/H runs at 157V at 1.33A, but cannot find ballast specs for it. I normally
should be able to calculate PF with just power, voltage, and current (PF=W/VA), but we have just proven that for some mysterious reason that method doesn't work accurately for discharge lamps (that calculated power factor does have applications that I have found, just not relevant here). Dead end.
So I can't get PF because I don't have ballast characteristics, and I can't get ballast characteristics because I don't have PF. Is this a standstill? Is there anything we can do for situations like the NA-1 or NE/H to get either PF or ballast characteristics from jus tthe running specifications so we can solve the puzzle?