A while back I developed a formula for computing the total (tangible) cost of ownership of light bulbs, it works for incandescent bulbs, CFLs, and LED lamps.
The formula gives dollars per megalumen-hours, given:
initial-dollars: the initial cost of the bulb in dollars
watts-consumed: how much power the bulb consumes in watts
average-lumens: how much light it produces at any given time, on average over its lifetime, in lumens
thousand-hours-lifetime: how long it lasts in thousands of hours
dollars-per-kilowatt-hour: the cost of electricity in dollars per kilowatt-hour
If you understand that a kilowatt-hour is the consumption of one thousand watts for one hour, or one hundred watts for ten hours, etc., then you'll understand the megalumen-hours concept too, it's the generation of one million lumens for one hour, or one thousand lumens for one thousand hours, etc. In other words, its a way of measuring the total light output of the bulb over time, just as kilowatt-hours is a way of measuring the total energy consumed by the bulb over time. I chose megalumens instead of just lumens because otherwise the numbers come out like 0.00000...
dollars-per-megalumen-hours = ( initial-dollars + watts-consumed * dollars-per-kilowatt-hour * thousand-hours-lifetime ) / ( average-lumens * thousand-hours-lifetime / 1000 )
I used "average-lumens" because both CFLs and LEDs slowly lose their brightness over their lifetime, and usually the end-of-life point is chosen to coincide with then the bulb has lost 30% of it's initial brightness (so it still has 70% left). Thus, in the examples below, for CFLs and LED lamps, I use an average-lumens value of 85% of the so-called "initial-lumens" (how bright the bulb is at the beginning of its life). This assumes a linear fallof of brightness over time, which I can't say is actually true, but it simplifies the formula greatly.
Here are some examples (all assuming $0.10/kilowatt-hour):
60-watt incandescent bulb, 800 lumens, 1,000 hours lifetime, $1.00 initial cost:
( $1.00 + 60 * $0.10 * 1 ) / ( 800 * 1 / 1000 ) = ( $1.00 + $6.00 ) / 0.8 = $8.75 / megalumen-hour
15-watt CFL bulb, 800 lumens (680 average), 6,000 hours lifetime, $5.00 initial cost:
( $5.00 + 15 * $0.10 * 6 ) / ( 680 * 6 / 1000 ) = ( $5.00 + $9.00 ) / 4.08 = $3.43 / megalumen-hour
7.5-watt LED lamp, 800 lumens (680 average), 50,000 hours lifetime, $100.00 initial cost:
( $100.00 + 7.5 * $0.10 * 50 ) / ( 680 * 50 / 1000 ) = ( $100.00 + $37.50 ) / 34 = $4.04 / megalumen-hour
Note that the CFL does come out a little better than the LED lamp in this case, but if the initial cost were dropped to more like $75.00, the LED lamp would start to have a better bottom line.
Note also that this formula does not consider less tangible factors like the cost of frequent changing of bulbs in difficult-to-access locations, or the cost to the environment of mercury escaping from improperly-disposed-of CFLs, or the additional CO2 that is put into the atmosphere to generate the extra electricity used by both incandescent bulbs and CFLs compared to LED lamps.
Edited by bobkart - Fri, 09 May 2008 08:56:38 GMT
Edited by bobkart - Sat, 10 May 2008 01:35:41 GMT
Edited by bobkart - Sat, 10 May 2008 06:31:16 GMT