The way I figure this is to first get the light intensity in the grow space to an acceptable level, then choose plant quantity based on the type of plants that are to be grown. More shorter plants for a "hedge" as we call it, fewer for larger top cola "competition" plants. I've done both.
I generally look at lumens per square feet, which for our purposes can be simplified into watts per square foot of light (hortilux super hps bulbs range from 130 to 150 lumens per watt - 600 W being the most efficient). Sodium lamps produce more lumens per watt if you get down to pulling hairs, so there may be a slight difference in halide and sodium. For me, the light concentration of the halide isn't as important, because it's used during the first stages of growth, so I base all calcs on the sodium. All my calcs are based on Hortilux Super HPS lamps, for something different, I'd ratio the lumens in the "other" lamp to the HPS Super, and use it as a correction factor.
If you don't have a defined area, then honing in on a number is difficult. Say you used some foam board, space blankets, mylar, or something to hold light to a space of 4x4, which is 16 square feet. With a 600 W lamp, you have 37.5 W/sq.ft., which is ok, but lower than what I run. With a 1000 W lamp, its 62.5 W/sq.ft., which I've found to be higher than necessary. You spend more watts per gram of finished product than if you kept it 40-50 W/sq.ft (my preferred range). I have seen folks use 60-70 W/sq.ft. with the intention of loosing yield efficiency (grams/watt) in exchange for some super killer budz, and they succeded. It was growers with a LOT of experience, and did a good job adjusting temperature, nutrient, and CO2 concentration to take advantage of the extra light intensity. That concept has its limits, too.
Once the light intensity is within a good envelope, your plant quantity selection is more important. If the light intensity isn't right, your not gonna get an optimum gram per watt harvest, anyway, so puzzling over the number of plants doesn't help much; they usually fill the space. My rule of thumb that's served me well for normal hydro grows is 1-2 square feet per plant. I've done as little as 0.6 square feet per plant, but it requires a lot of extra work to get an optimum harvest due to the excessive foliage and difficulty reaching plants in the middle of the 40 sq ft garden. That would probably be good for small plants with a single large top (maybe what they call lollipops around here). The 2 sq ft and even higher, I usually reserve for taller plants under 1000 W lamps (good penetration). For potted soil plants 2 or more sq feet per plant would be more appropriate. It's been awhile since I've seen any soil gardens except outdoor, so maybe someone else chimes in with some info on this. I'm sure there are a lot of opinions on how to do this part. My methods are old-school.
If I were doing an 8x8 actually filled with hydroponic plants I'd use 4 each 3x3 trays positioned to leave 2 ft walk spaces between them, plants will fill the gaps, but you can still get in there to work on em or prune if you need to do so. I'd run 2 dual lamp fixtures with (1) 1000W & (1) 400W each on a light rail, so you can get Sodium-Halide Combinations. If just using HPS with no light rail, I'd run (4) 600W Hortilux Super HPS's, one over each tray with 8-12 plants per tray. In your image in the original post, it looked like bucket hydro systems, which would require more space that what I've allotted for each plant. You could get away with 2000 W or so and still get a good crop, buds probaby wouldn't be as impressive, but you could see an increase in grams/watt if the plants are properly pruned and cared for. You may have to account for entry/exit/work space. You gotta have room for all the work you need to do. I usually have the plants walled in with other space for the labor involved.
Hope this helps. Peace.
