[Greenbuilding] Water heater timer energy savings?

[Nick Pine]

>This water heater http://m.lowes.com/pd/Whirlpool-50-Gallon-240-Volt-6-Year-Regular-Electric-Water-Heater/50397576 has an EF = 0.95 energy factor, ie it uses Qdm Btu/day, about 5% more than 
the average daily useful water heating energy https://en.m.wikipedia.org/wiki/Energy_factor  as tested in a 67.5 F room with 6 64.3 gallon draws of 135 F water heated from 58 F in the first 6 hours of the day, with an 18 hour rest period after that.

Oops. https://en.m.wikipedia.org/wiki/Energy_factor says:

"During the test 64.3±1.0 gallons of water are drawn from the water heater in six equally spaced draws that begin one hour apart."

After I calculated the 88 F water temp after 6 hours and realized that 6x64 gallons is a lot of hot water for a family and reflected on the R1.82 wall insulation calc, I realized that the total draw is 64.3 gallons, which makes the useful water heating energy Qu = 64.3galx8.33lb/gal(135-58) = 41243 Btu, approximately. And EF = 0.95 = Qu/Qdm by definition, so Qdm = Qu/0.95 = 43413 Btu, and the standby loss with no water draws is 43413-41243 = 2170 Btu/day, approximately, ie 0.64 kWh/day, or 1628 Btu during the 18-hour rest period, when a timer might help save energy.

With no timer, 1628 Btu = 18h(135-67.5)G makes the water heater's thermal conductance G = 1.34 Btu/h-F. With 50 gallons of water, thermal capacitance C = 50x8.33 = 416.5 Btu/F, approximately, so the cooling time constant RC = C/G = 416.5Btu/F/(1.34Btu/h-F) = 311 hours, so with a timer, the water would cool from 135 F to 67.5 + (135-67.5)e^(-18h/311h) = 131.2 F in 18 hours. Reheating it to 135 before the next draw would require 416.5(135-131.2) = 1583 Btu. So the timer saves 1628-1583 = 45.3 Btu/day, or 1.9 Btu/h or 1.9/3.412 = 0.55 watts, on a continuous basis.

How long would it take this $21.57 R10 water heater blanket to pay for itself at 15 cents/kWh? http://www.lowes.com/pd_24399-1410-SP57/11C___?Ntt=water+heater+blanket&UserSearch=water+heater+blanket&productId=3133229

Nick
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