Fluoros and HPS Strength question about inverse square law, ect.

Hey guys first post. I haven't started growing but I have equipment and plan to start in a week or so.

I have a question about lighting though.

A 400w HPS Light emits around 50,000 lumens

I'm going to use 4- 48' 2700k T5 Fluoros for flowering. In total, they use I believe 216w and emit 20,000 lumens.

Since you can't keep a HPS that close to the plant, doesn't the plant only receive a smaller portion of the 50,000 lumens than they will if I have my 20,000 lumens up close to the plant because of the inverse square law? (I'm going to lst by the way)
Why is the HPS that much better than fluorescents then?

And also, do you guys think that that set up is enough for 4 plants? 54w for each plant, 5,000 lumens? Am I pushing it? Thanks alot guys

great questions. what matters with grow lighting is both its intensity in lumens per square foot and over how many square feet it can produce that intensity. for instance your 400 watt light at 55000 lumens gives you good intensity of 5500 lumens per square foot for 9 square feet at 18" from the light ( not ten square feet because of light losses for the light that's reflected). each of your four fluoros can cover slightly less than one square foot. so in other words the lumens aren't wasted if you have plants that occupy all of the square feet of coverage. the inverse square law refers to the intensity of the light as it gets further from its source in a spherical wave. you have just as many lumens but they are spread over more area/volume. the t5's produces 93 lumens per watt while the 400 produces 138 lumens per watt. even though those t5's are the most efficient fluoros, and the 400 is one of the least efficient hps bulb, the hps is still far more efficient than fluoros at the same wattage.

as for what intensity intensity to shoot for: 5,000 lumens per square foot is good, but 7,000 lumens is not too much and if you can fit, afford and cool that much light you should go for the higher intensities.

thanks alot desert that helped a lot, +rep

Its best to just think in lumens/sq ft like desertrat is saying. I have my 150w hps with 16,000 lumens covering 1.5x1.5.. if that.. closer to 1x1. So I'm 7-16,000 lumens per sq ft. If I wanted to expand my grow area to 3x3 then I'd be at 1700 lumens sqft.

I dunno I still confuse myself when I think about it too hard.