RP wrote:
Thus, if the overnight (set back) runtime is reduced by an amount of time
that is twice the recovery time with heat strips enabled), then energy
is saved over not setting back...
Thus? :-)
Thus, yes, at some higher COP and/or warmer climate the trend will reverse.
That's why I said in summary that economy depends upon the system 
I don't quite see a "thus" there. Would you further explain your logic?
I'm sorry, that won't be possible. I can however add more conclusions at
will. It's quite easy once you get the hang of it
My friend Rich says he can easily supply multiple inconsistent conclusions.
I'm not in the mood to drag in formulas at this point in time, having
worked all weekend, till dark hours. IOW, I'm too damned tired
Perhaps later, when you have rested.
You've probably worked through this already, so if you would, could you
please provide some math to analyze the set-back savings of various COP
systems with and without resistance heat enabled?
Well, we might agree that night setbacks always save energy with heat strips
switched off, even though that requires longer reheating after the setback,
but a longer setback with a faster recovery using strips might save more,
if the house can stay cooler longer. This wouldn't apply to houses with
zero or infinite thermal mass, but it might with a finite mass.
In scenario 1, keep a house with G = 200 Btu/h-F of thermal conductance at
70 F for 8 hours on a 30 F night with 8h(70-30)200 = 64K Btu from a heat
pump with a 2:1 COP, using 64K/2/3412 = 9.38 kWh of electrical energy.
In scenario 2, the house has C = 10K Btu/F of thermal capacitance and
an RC time constant C/G = 50 hours, so it cools from 70 F at midnight
to 30+(70-30)e^(-8/50) = 64.1 at 8 AM. The house returns instantly to
70 F at 8 AM, with powerful strip heaters that consume (70-64.1)10K
= 59K Btu, or 17.3 kWh, almost twice scenario 1.
In scenario 3, the house has a wimpy 10K Btu/h heat pump with a 30+10K/200
= 80 F Thevenin equivalent temp and no strip heaters. It cools to a minimum
temp T (F) in t hours and reheats in 8-t hours, so T = 30+(70-30)e^(-t/50)
and 70 = 80+(T-80)e^(-(8-t)/50) and t = 1.7 h and T = 68.7 F. Reheating for
6.3 hours takes 6.3x10K/2/3412 = 9.23 kWh, with a small setback savings.
More typically, with C = 5K and G = 500 and RC = 10 hours and a 60K Btu/h
heat pump with a COP of 3 and a 30+60K/500 = 150 F equivalent temp, we
would use 8h(70-30)500/3/3412 = 15.63 kWh in scenario 1. In scenario 2,
the house would cool to 30+(70-30)e^(-8/10) = 48.0, and the heaters would
consume (70-48)5K/3412 = 32.24 kWh at 8 AM. T = 30+(70-30)e^(-t/10) and
70 = 150+(T-150)e^(-(8-t)/10), so t = 6.0 h and T = 52.0 in scenario 3.
Reheating takes 2.0x60K/3/3412 = 11.9 kWh, for a big setback savings.
Without strip heat enabled it *seems* obvious that the monetary savings
of setting back would be greater with the lower COP system. IOW, with a
COP of 1, you have effectively the economy of straight strip heat, in
which case setting back definitely helps the pocket book.
Some people say the COP of a heat pump can be less than one, but that
seems hard to believe. OTOH, they do wear out.
OTOH I'd be very grateful if you could prove otherwise, as my wife is
a setting-back fanatic and I'm tired of waking up to a cold ****er.
I suppose I could shorten it a bit, but hanging it in the water easier
than aiming when you haven't had your coffee yet.
You might enjoy
http://www.homeclick.com/showpage.asp?itemid=3D202929, or
http://www.cleanbutt.com/PRODUCT.ASP, with optional wireless remote control.
Nick