For the pool you better off to build a solar heater- to extend swimming season and buy him a variable speed pump to help with electric bill. Much cheaper overall.
Back to your project- those bulbs still convert about 10% of electric power into light, the rest will be converted to heat (additional fans to cool them off?). The heat is infrared and not useable by panels- panels have narrow spectrum band in the visible part. 400Wt metal halide will produce total 40Wt flow of light which will be spread all over the place. 400Wt is how much it consumes, not how much it produces . If you put it in some reflector (hang it in focus plane of parabolic pipe with fans on both end to move the air through and it will form more or less parallel beam of light) so at least 80% will reach the panel then the panel will extract 20% of electric power out of it. Your overall efficiency: 10% x reflector efficiency (80%) x 20% = 1.6%. BTW 50W panel means how much it produces, not how much light it can tolerate. Given panel's efficiency 50W panel requires 250W of light flow- you'd need about 8 those 400Wt projectors to lit it up all using some kind of reflector to direct their output. We're talking about 3kW power consumption- at 110V AC you'd need couple standard 15A outlets connected to independent lines to feed the beast. I'd like to come to see it light up, must be spectacular show- it will be really, really bright. You're trying to compete with the Sun after all .
Back to your project- those bulbs still convert about 10% of electric power into light, the rest will be converted to heat (additional fans to cool them off?). The heat is infrared and not useable by panels- panels have narrow spectrum band in the visible part. 400Wt metal halide will produce total 40Wt flow of light which will be spread all over the place. 400Wt is how much it consumes, not how much it produces . If you put it in some reflector (hang it in focus plane of parabolic pipe with fans on both end to move the air through and it will form more or less parallel beam of light) so at least 80% will reach the panel then the panel will extract 20% of electric power out of it. Your overall efficiency: 10% x reflector efficiency (80%) x 20% = 1.6%. BTW 50W panel means how much it produces, not how much light it can tolerate. Given panel's efficiency 50W panel requires 250W of light flow- you'd need about 8 those 400Wt projectors to lit it up all using some kind of reflector to direct their output. We're talking about 3kW power consumption- at 110V AC you'd need couple standard 15A outlets connected to independent lines to feed the beast. I'd like to come to see it light up, must be spectacular show- it will be really, really bright. You're trying to compete with the Sun after all .
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