I have a pool in my new house which I would like to keep heated to
about 80F During weekends and other times when we want to use it.
With raising Natural Gas prices I would like to make an excel
spreadsheet that will allow me to keep an EXACT TAB (within say $10)
of how much it costs me to heat the pool at any given time.

The answer I'm looking for should have equations that I can USE IN
EXCEL to plug in variables such as outside temperature, average wind
speed, current cost of cubic feet of gas, etc.

The equations can use BTUs, calories or whatever else to calculate the
heat loss etc, but everything in the end must has to be converted to
cubic feet of gas needed, so I can then multiply that by the current
cost and get a total.

Bonus will be given (on top of the "normal" tip) if you produce the
spreadsheet yourself and if it includes extras such as "time to pool
the heat to X degrees F starting from current water temperature. But
this is not required for a valid answer.  As long as I can use the
equation in excel we are good :)

Examples of uses for the proposed spreadsheet:
1) temperature outside is 69F, water temperature is 68F. Its a
Thursday and I will want to keep the pool heated until Sunday evening.
Equations should calculate the energy needed to get the water
temperature to the proposed 80F and keep it there for the next 72
hours taking into consideration:
a) heat lost to the air
b) heat gained from sun
c) heat lost to concrete? (might be minimum, or hard to calculated if
I need to know the temp of the concrete)
d) much lower temperature at night (60F) than during the hottest time of day 79F
e) anything else I'm not aware of that would affect the ultimate
total, the COST of all that energy in cubic feet of natural gas.

This is a drawing I made of the pool.  
http://www.fotosrv.com/img/1128045606Pool_size.jpg

I should mention there is no cover (and I don?t plan to install one),
the pool is surrounded by a 9' feet fence so wind speed on the surface
of the pool is rather low.  Pool is not shaded at all so it does get
hit by the sun in full force on sunny days. I live in zip code 07410
in case you want to use my current temperature for a sample equation.

PS: I was not sure how to price this question, it seems to me that
someone that knows about thermodynamics should be able to come up with
the equations fairly easily, but I could be wrong, if so leave me
comments.

Please remember, I MUST BE ABLE TO USE THE EQUATIONS  IN EXCEL! 
Answers with equations with weird greek letters that I cant easily
transfer to excel wont be accepted :-)

---

Clarification of Question by zexion-ga on 30 Sep 2005 06:09 PDT

That is helpful Brix24 at least I have an idea of the over all costs,
but I really need the equations so I can do a day by day chart for the
cost of heating the pool, so I can set some rules for the whole family
upfront and save as much money as possible (without adding a cover).

This comment does not give a way to do your calculations, but there is
some interesting information at this Dept. of Energy site:

http://www.eere.energy.gov/consumer/your_home/water_heating/index.cfm/mytopic=13180

There they show estimated costs for gas heating of a pool of 1000
square feet, with an 80% efficient gas heater, at 3 different
temperatures, with and without a pool cover, and with gas costing
$0.50 a therm. You could get a rough estimate of your total cost for a
season from this table.

You would start with the costs for New York and multiply those costs
by 3/4 because your pool has a surface area of 752 square feet. You
could adjust for the price of gas by using the factor (current cost of
gas per therm/$0.50). Below the table, there is a formula to use if
your heater has an efficiency different than 80%.

This result just gives you an overall season estimate; it's probably
not too good for a month-to-month estimation because wind speed could
vary from month to month and the outdoor temperature would certainly
vary from month to month.

These Dept. of Energy estimates does not take into account variations
in the area of the sides that are in contact with the ground.

The site don't seem to say how they made their estimates, which could
have been helpful in getting the calculations you want.

The Dept. of Energy has a separate site that indicates that 78 degrees
is probably for competitive swimming; young children and the elderly
may need either the 80 or 82 degree temperature. This information is
at

http://www.eere.energy.gov/consumer/your_home/water_heating/index.cfm/mytopic=13300

Oops! The formula at the bottom of the table is for cost savings when
replacing a gas heater.

To correct the Dept. of Energy estimates for your heater, just use the
factor (80% / your heater's efficiency) instead.

Zexion,
I understand that you are not considering a cover for the pool, but
nonetheless, a floating cover with a dark surface would definitely
help reduce heating costs and probably reduce cleaning of pollen and
leaves.

http://www.geothermie.de/egec-geothernet/ghc/21-3art2.pdf

Here are two UK sites about solar pool heating that could also be of
interest, maybe there are US sellers, but I haven't yet found any:
http://www.saferpools.co.uk/solar_panels.htm
http://www.btinternet.com/~poolclean/swimming-pool-solar-heating.htm

http://www.nbws.com/catalog3.htm
http://www.vulcan-hp.com/howitworks.php

Okay, here are the risks:
http://poolcoversusa.com/floating.html

Enough on the subject, Myoarin