Home Heating

Note: you must allow your web browser to run Javascript for this calculator to work.

This is a simple calculation to estimate the cost and payback for installing a geothermal heat pump in your home. The calculation of the winter heat loss out of your home is based on your known consumption of oil over an average winter.

The calculation is intended to compare oil heat to a new heat pump installation, under the exact same temperature conditions. If you change the average inside temperature of your home, or if the outside average winter temperature changes, these results become less and less accurate, because they are based on the amount of oil you consumed under a specific set of winter temperatures.

Fill in all the data in the input table, then click the CALCULATE button.

Don't break anything.....

Notes:

Net oil heat value = 115,000 BTU/gal and it already includes a 83% efficiency factor assumed for your oil burner and heating system.

Gallons consumed: this is a critical number .... be sure it is correct for the time span you enter. Do not include gallons delivered to your house but are still in your tank!

Time span: the wintertime months that you burned the gallons entered above.

T(avg,inside ⁰F): the average 24 hour temperature of your home during the entire winter time span you entered above. You will have to do some thinking about this and averaging day and night as well as whatever "zones" you have around your home.

T(avg,outside ⁰F): the average 24 hour outside temperature during the winter time span. There is a link below to a website that lists these for your zip code.

T(min,outside ⁰F): the minimum outside temperature recorded during the winter time span. There is a link below to a website that lists these for your zip code.

Cost of oil ($/gal): use the current or the future value, depending on why you are doing this calculation.

Heat pump COP: the coefficient of performance of the heat pump you are thinking of installing (get manufacturer's data). There are some heat pump links below also.

HP installation cost: the total quoted cost of installing a heat pump system.

Electric $/kW-hr: the cost of electricity to you (check your bill). This is important for the heat pump operational cost calculation .... must be accurate.

The Output Data Table: if you don't know what a term means (for example, "UA") just ignore it.... it's probably a term only an engineer would want to see.

References

• Weather Base (local outside temperatures)
• Climatemaster
• Waterfurnace
• FHP Mfg.

These are my sample calculations that lead to the Javascript calculator shown above.

2007-08 Winter

The intent here is to show how I would calculate the heat transfer out of or into a home, based on a known oil consumption rate.

References

• Weather Base (local outside temperatures)
• Climatemaster
• Waterfurnace
• FHP Mfg.

Input Data (change as necessary for your case):

• mid Sept.2007 - mid Apr.2008 : 24 * 7 * 30 = 5040 hours
• Average outside temperature (24 hrs/day) = 40F (from weather data site)
• Assumed constant inside temperature (24 hrs/day) = 66F
• Heating with #2 oil: 115,000 BTU/gallon ( net, includes .83 eff factor)
• Heating system efficiency = 83% (new, hi-tech burner in good clean condition)
• Actual oil consumed during this period of time = 2600 gals

Comment: this method (which includes an efficiency) calculates the average heat transfer in and out of the walls, roof, windows, doors over a long period of time. There is additional energy that is wasted (1.0 - efficency) and does not participate in this heat transfer because it is never delivered into the house.

Calc's

• Total heat loss = 2600 * 115,000 = 299E6 BTU's (this is the net heat energy delivered to the house by the heating system).
• Average heat transfer rate = 59,325 BTU/hr for winter 7 months
• If the 2600 gals were consumed in 6 months, average heat transfer rate = 69,213 BTU/hr
• Again T(in) = 66F & T(out) = 40F .... heat rate changes with T(in) - T(out)

Comments

To calculate the heat transfer rate at different temperatures, note that

Heat Rate = Q = U * A * [T(in) - T(out)]

where U * A is simply a numeric constant for the building design and for last winter's average wind levels and daytime sunshine levels and nightime radiation cooling levels. In general this is a very constant value (when averaged) for a given building, in a given location, through a given span of months.

U is the "overall" heat transfer coefficient for the house; A is ths total surface area between the inside T(in) and outside T(out).

You can calculate U * A from the known data In this case ( assume 7 months for burning the 2600 gals oil)....

U * A = 59,325 / (66 - 40 )= 2282 BTU / hr / DegF

You can now approximate a Summer calculation, using the same U * A, to cool the house from T(out) = 90F to T(in) = 75F,

BTU/hr = 2282 * ( 90 - 75 ) = 34,226 BTU/hr

# Addendum .... Coldest Day Heat Required #

The calculation above was aimed at determining the average amount of heat lost during the average winter day. To play it safe for the worse case, you should over-design the heating system to provide enough warmth for the coldest day (0⁰F ?) , not the average day (40⁰F).

For this purpose, you would do this....

(-0F) Cold Day Heat Loss = Q = U * A * [T(in) - T(out)] = 2282 * ( 66 - 0 ) = 150,612 BTU/hr.

(-20F) Cold Day Heat Loss = 2282 * (66 - (-20)) = 196,252 BTU/hr

This would not be the winter average heat transfer loss, but the over-designed system would keep you warm on the coldest day.

If you designed your heating system to the average (40F) heat load value of 59,325 BTU/hr, the warmest you could get your house on a (-20F) day would be ....
59,325 = 2282 * (x - (-20) )

X = 6F ! ! which is why the system has to be about 3X larger than the average calculation suggests.

The Cost of Operating a Geothermal Heat Pump

• Assume COP = 3.75 (Wikipedia, geothermal heat pumps)
• Assume total ( average over a winter, 24 hrs/day) heat energy delivered to the house must be 25,000 BTU/hr (7.33 kW). [See this calculation.]
• The electrical energy required to run the heat pump is 25,000 / 3.75 = 6667 BTU/hr = 6667 / 3412 = 1.95kW
• That's 1.95 * 24 * 30 = 1407 kW-hrs / month
• At my current billing rate (Leominster), it would cost $223 / month to run the heat pump (in addition to my normal electricity use).
• The cost of (current) oil would be...
  (25,000 * 24 * 30 /115,000) * 4.65 = $728 / month.
• That's a savings of 7*(728-223) = $3535 / winter
• If the heat pump system costs $35,350 to install (wild guess), you would not breakeven on the expense for 10 years (it would be 10 years before the system broke even in cost).
• The advertised average life of heat pumps is 22 years.

Electric Heat vs. Oil Heat

• Current electric cost = .159 $ / kW-hr
• Current oil cost = $4.65 / gal
• Oil generates 115,000 BTU / gal (net, including .83 eff factor)
• House requires 25,000 BTU / hr in winter
• Conversion factor: [BTU / hr] / 3412 = kW

Cost of Oil: 25000. * 4.65 / (115000. ) = $1.01 / hr

Cost of Electric Heat: [25000. / 3412.] * .159 = $1.16 / hr

Wood Heat Value

In the equivalent # of chords calculation shown in the Javascript calculator, I used the average 25,000,000 BTU/chord heat value for dried wood, from tha data below. Multiplied that by the burning efficiency also noted in the calculator above.