TURTLE wrote:

If you turn a hvac system off less than 8 hours. It will cost you more
money to recool the house from a very high temperature to the lower
temperature than just moving up to a higher temperature on the thermostat.

Newton died in 1727. These days, few people argue with his Law of Cooling.

How would the house get from 70 F to 105 F in 8 hours on a 100 F day?
Assuming it could (which would save lots of AC energy), and assuming
it had reasonable insulation, it would have very little thermal mass,
so the AC could cool it back to 70 F very quickly.

Now if you have oversized hvac system like 5 tons on 1,500 sq. ft. house.
Your answer would be ok, but a properly sized system would cost you big
time on a 4 hour down time.

The setback would still save energy, unless the AC becomes a lot less
efficient (has a lower COP) with a higher indoor-outdoor temp diff.

A 1500 ft^2 house with 300 Btu/h-F of thermal conductance could warm from
70 F to 105 F in 8 hours on a 110 F day if RC = -8/(ln((105-110)/(70-105)
= 4.1 hours, which makes C = 4.1x300 = 1200 Btu/F, not much. A 36K Btu/h
AC might cool the house from 105 to 70 F in (105-70)1200/36K = 1.2 hours.
Keeping the house 70 F for 8 hours would require 8(110-70)300/36K = 2.7
hours of AC operation... 1.2/2.7 is a 55% energy savings.

This all looks good on paper but in the real world with a over sized hvac
system as you say a 3 ton on 1,200 sq. ft. house. A properly sized hvac
system will have a 1.5 or maybe 2 ton at most on the 1,200 sq, ft. house.

OK. Let's try 1.5... An 18K Btu/h AC might cool the house from 105 to 70 F
in (105-70)1200/18K = 2.4 hours. Keeping the house 70 F for 8 hours would
require 8(110-70)300/18K = 5.4 hours of AC operation... 2.4/5.4 is a 55%
energy savings, not unlike the previous 55% savings.

Now you say the 3 ton 36K btu rating is used in your calculation here.
All hvac system are rated at 95ºOutdoor temperature and when the
ambiant goes above the 95ºF level your BTU rating falls a good bit
to maybe 31K or 33K btu's at 105ºF outdoor temperature.

Good info. While using the same electrical power? What happens to the COP?

How is latent heat rated? I sometimes wonder if a house would cool quicker
after a setback if the owner sprayed some of the inside surfaces with water.
The cold side of the AC would transfer heat better with condensation than
without, and the house surfaces would cool more quickly with evaporation
than without, and 400 cfm of moist return air carries a lot more heat than
dry air. The water wouldn't add to the net cooling load, since it requires
heat to evaporate. It might act as a catalyst, speeding heat transfer.

Now with all your calculations that the hvac system is perfectly tuned and all
coil are clean and serviced regularly...

Of course. By certified HVAC criminals. ("That'll be $8764.32, Mr. Sneedley.
I knocked off $10 for the blowjob.")

There was some research done in California on systems being properly charged
with freon, Clean coils, and running at what they should be putting out. More
than half was not operating at what they should have been and was not putting
out the BTU rating stated by the manufactor. A lot of the system checked was
running at about 70% of what they should be putting out.

This criminal negligence may not have much to do with
whether AC setbacks save energy.

...I personally have a 2,250 sq. ft. home and cool it with a 3.5 ton
14 seer system.

Well-maintained, no doubt.

I have let my cooling system be off for being gone for about 8 to 10 hours
and on a 105ºF day. My house inside went up to about 98ºf inside and
when i turn on my perfectly tuned system on. It took 3.5 hours to pull the
house back to 72 ºF.

Maybe you have some unshaded windows and lots of insulation
and lots of pet rabbits or PCs.

Let's review your claim:

If you turn a hvac system off less than 8 hours. It will cost you more
money to recool the house from a very high temperature to the lower
temperature than just moving up to a higher temperature on the thermostat.

You mentioned money, but you didn't mention time.

The first 2 hours you can not stay in there for it being too hot.

Maybe you need a timer to precool the house before you get home.

Now if i would install a over sized hvac system and have a 5 ton or so. It
would not be but a hour or so to get back down to 72ºF inside but I would
have to deal with high humitity in the house and will have to run my system
at lower temperature than 72ºF or maybe down to 65ºF to get the water
vapor out of the house. With a 90%RH a house at 60ºF will feel very warm
inside. With a 10%RH and 95ºF inside the house will feel very cold...

The ASHRAE 55-2004 comfort standard says most people would find 90% RH
at 60 F "very cold" (Y = -3.2, with 99.6% of people dissatisfied) and
10% RH at 95 F "very warm" (Y = +2.8, with a 97.4% PPD.) Maybe you need
a comfortstat vs thermostat. It might automatically lower the air temp
to compensate for a higher RH or Mean Radiant (wall) Temperature.

Now here is one that will never fit with your calculation on the cooling
of the house. All properly designed and sized hvac systems are designed
and installed to have a 90% run time which are designed to be run all
the time and not turn them off.

At the local summer design temp, which occurs 1% of the time?

On a properly sized / designed hvac system if you started at 100ºF
inside temperature could easily have a 8 hour run time to get it cool
enough to be called cool enough to live in it.

A house like this would likely have lots of thermal mass, so it seems
unlikely to get to 100 F during an 8 hour setback...

Now you had said a house inside with no air on will not go up to 100ºF+
with in 8 hours -- out in the direct sun light, 105ºF outdoors, Roof
area temperatures running about 190ºF with the direct sun light on it,
house with the average R-19 rating on it, and most all houses are not air
tight. In 8 hour, I would be surprized to not see it 100ºF.

With little mass, and some unshaded windows and internal heat gains. If the
owner and builder weren't crazy, the house and roof would be white, in a hot
climate, with a radiant barrier under the roof, eg Norbord's foil-faced OSB.

Now one last point here. Your calculation will be for the air inside the
house and not for the metal , cloth couches , Rugs / carpet, and furniture
which will hold and release heat over the next 4 to 8 hours and you will
have to remove this extra heat held by these items as the next 8 hours
of operation time goes.

No. My calc included the entire thermal mass of the house. A 1500 ft^2 house
has 12K ft^3 of air that weighs about 900 pounds. Its specific heat is about
0.24 Btu/F-lb, so the air only has 216 Btu/F of capacitance... 3000 ft^2 of
1/2" drywall would add another 1500 Btu/F of capacitance, and so on.

Nick