Like you, my head was about to explode when I started looking at all this. But after a while, it all seemed to make sense. Have a look at the Forward Voltage vs Forward Current graph on page 21 of the LM561c spec sheet:
http://www.samsung.com/global/business/business-images/led/file/product/lighting/201511/Data_Sheet_LM561C_Rev.3.2.pdf
LEDs are resistors, so the more current you put through them, the more resistance they offer.
According to the graph, when you put 80ma through each diode (40% of their rated power), their individual voltage drops 2.8v. For four strips in series, that would be (2.8v x 16s = 44.8v) x 4 boards = 179.2v total, and you would use (0.080a x 9p) 0.72a to power them for a total wattage of 129.02w.
Have another look at the graph where the line intersects 160ma and roughly 2.94v. Do the maths and you get 47.04v for each board (188.16v total in series) @ 1.44a for 270.9504w.
So do you see how the more current you put through each board, the higher the voltage drop?
It's not linear - you would at first expect that double the current equals double the wattage, but in fact the wattage has gone up by more than 2x because the individual voltage has also increased.
For the sake of drivers (and hopefully I won't get my figures mixed up this time!), a HLG-240H-C1400a would drive the first example (it would be 0.2v over the 179v max, so would likely
just handle it), but not the second example - because even though it can provide 1.4a, it can't provide it at 188.16v. You need to find another driver. Also, the total wattage (271w) is a giveaway, because the 240 series drivers are only rated to 240-250w, though I understand they will actually put out a little more.
Each strip would only drop 48.4v if you were running them at max 1.8a, but at a more conservative (recommended) 1.12a, they drop about 46v - that's where the 1.12a/46v figures come from in the Samsung spec sheet for each strip.
I chose a 240 series driver to power four strips for three reasons: cost-effective (2x 240s appear to be cheaper than 1x 480); a smaller driver is more efficient than a larger driver powering the same number of boards (from my understanding); and lastly, I didn't really want to drive my boards much higher than 70%, so the 240H-48 in parallel fits the bill perfectly. In fact, I'll probably only be driving my boards at about 60%, so I could have gone with the 240H-C1050A in series, but the 48 gives me the option of a bit more available power if I need it, even though I will dim it down.
My suggestion? Run 4x strips on a 240 series, then when you buy another four strips, buy another 240 series driver - cheaper than 8x strips/1x480 with a lot more flexibility. You could run two channels (different CCT strips) etc or whatever you want.
I hope that all makes sense. I'm pretty sure my numbers are right this time