@Ash
Alright I did some more figuring.
This equation works very reliably, and I would like to use it, but I have some questions.
I was using this equation in conjunction with ohm's law to calculate desired ballast impedance when given lamp voltage, circuit voltage, and lamp current.
This consistently overshot the specified impedance necessary for the lamp based on datasheets, but very precisely. For MV, it was almost exactly 20% overshooting, for MH it was more or less 15% overshooting, and for HPS it was pretty consistently 10%. I took the averages of all of the overshots and then the inverse and got these constants to multiply with the results to get the right approximate answer:
MV: 0.831
MH: 0.873
HPS:0.913
This is okay, all I have to do is remember these numbers when calculating. But I want to know where they came from. Is this the power factor of the discharge itself? That is what I am thinking, but I don't know for sure. I can't think of any other reason it would be so consistent across different wattages but so different between different HID technologies. I have yet to try this for fluorescent and LPS lamps but I might do that later.
Thanks again.