Lighting Calculations - Notes

Lighting Calculations, Round 2

Per the Wikipedia article...

1120 W/m2 of direct and indirect sunlight hit the ground.
1050 W/m2 of direct light.
43% is visble (400 to 700 nm)

luminous efficacy is about 93 lumens per watt of radiant flux.

Direct light = 97,650 l/m2 of illuminance.
Visible light = 41,989 l/m2

1 m2 = 10.7639 sqft

DWC: 20 sqft = 1.85806 m2
GB:  16 sqft = 1.48645 m2

Total required illuminance
DWC: 78,018 lumens
GB:  62,414 lumens

lumens per sqft:  3900

This means that we need around 8000 lumens per linear foot of grow space, since the spaces are 24 and 30 inches deep (respectively).  Four 2000 lumen elements, or eight 1000 lumen elements, would provide a sufficient quantity of light, plus we can balance out the wavelengths to provide a nice, full spectrum.

This would need to be repeated each linear foot, or 8 times, yielding around 32 or 64 (respectively) LED elements per grow space, to meet the lighting target.

A search on Digikey provides some ideas on wattage.  Efficiency will be between 80 and 140 lm/W. 80 lm/W buys us 1005 lumen elements, and 64 of those will provide 64320 lumens.  0.0125 (1/80) W/lm times 64320 lm = 804 watts for the smaller array.  Going with 140 lm/W in the search provided options for both 1005 lm and 1770 lm elements, so maybe we'll go with those instead.

Current electrical rate (assume the worst): $0.12047 / kWh

Assume 30 days per month, 12 hours per day of run-time.

Here are the array figures:

DWC:

• 78018 target lumens
• LED quantities:
• 78x 1005 lm LEDs, or
• 44x 1770 lm LEDs
• Cost per LED (best price, rough-estimate):
• $4.00 per 1005 lm element ($312.00)
• $16.51 per 1770 lm element ($726.44)
• Power Consumption:
• 78 * 0.8 A * 9 V = 561 W for 78390 lm (139.7 lm/W)
• 44 * 1.05 A * 12 V = 554.4 W for 77880 lm (140 lm/W)
• Energy Cost (with above assumptions)
• 78 element array = $24.33 / month
• 44 element array = $24.04 / month

GB:

• 62414 target lumens
• LED quantities:
• 62x 1005 lm LEDs, or
• 35x 1770 lm LEDs
• Cost per LED - same prices as above
• 62 elements = $248
• 35 elements = $577
• Power Consumption:
• 62 * 0.8 A * 9 V = 446.4 W for 62310 lm
• 35 * 1.05 A * 12 V =  403.2 W for 61950 lm
• Energy Cost (with above assumptions)
• 62 element array = $19.36 / month
• 35 element array = $17.49 / month

Commentary
The above figures are rough estimates.  Specifically, the energy costs are LOW-END estimates, meaning the final costs will be higher once losses in the AC to DC conversion are taken into account.  Also, the arrays are not necessarily geometrically optimal, meaning that 44 elements will not fit neatly into 8 linear feet of space (5.5 elements per linear foot).  A staggered design will be beneficial nonetheless, so this isn't necessarily a problem.

Output values for the lighting was taken from flux at 85 degrees C.  Lower temperatures should yield better light output (more efficiency).  Also, the test current was used, but max current ratings can be upwards of double or worse.  Higher current usage means less efficiency and higher power bills.

The costs above also do not account for: the LED drivers, wiring, heat-sinks, and LED mounts.

Return on investment will be realized when we save $50 / month on our groceries (really $43.69, but I'm throwing in a wild-ass-guess for the pump and aerator energy costs).


Further reading

• Sunlight
• https://en.wikipedia.org/wiki/Sunlight
• Tables for direct solar radiation at northern latitudes:
• http://www.fs.fed.us/pnw/pubs/pnw_rp142.pdf