Charles - copying my post in another forum. You can't figure heat pump calcs the way you are doing. I know the post is long, but by the end you'll have a better concept of what goes on.
Heat pump efficiencies and use explained
Covering the basics and other fuels is the best way to start. A BTU is a British Thermal Unit, the amount of energy required to raise the temperature of one pound of water one degree Fahrenheit.
Fuels have differing "densities" of energy. A partial list includes:
Kerosene - one gallon has 134,000 BTU available as heat when burned.
Propane has 91,500 BTUs in each gallon
Gasoline has about 110,300 BTUs per gallon
Dried firewood has about 7870 BTUs in a pound of wood
Electricity has 3413 BTUs in a KWH (kilowatt hour) A kilowatt hour is what is required to light a thousand watt lightbulb for one hour.
If fuel is used only for its heat value it is fairly easy to compare the relative costs of using each fuel. To make the resulting figures easy to read and interpret I use 341300 BTUs as the standard amount. That equals 100 KWH of electricity.
If electricity costs ten cents per KWH, then 100 KWH will cost $10. That would be the cost if you used a resistance space heater to get 341300 BTUs. Resistance heating with electricity has an efficiency of 1, meaning that every BTU is extracted from the electricity you are billed for, no more, no less.
An unvented propane heater or cooktop also has an efficiency of close to 1. If propane costs $2.10 per gallon, the same amount of heat would cost $7.83
A kerosene lamp likewise has an efficiency of close to one, so the same heat from an unvented kerosene heater or lamp would cost about $8.91 if the price of kerosene was $3.50 per gallon.
(Burning fuel has a real efficiency of less than one because make-up air has to come into the home to continue the combustion, and heated air has to be exhausted to create space for it.)
Costs increase if efficiency drops. For instance, a fireplace may be only 10% efficient, meaning 90% of the heat goes up the chimney. If the cost of wood is a penny a pound, you would need 434 pounds of wood to get the same usable heat! You would of course spend $4.34.
However, if you use a relatively efficient wood stove that has a 50% efficiency, you would use only 87 pounds of wood, and pay $.87 in fuel cost.
To calculate the relative cost of heating, use this formula:
341300 divided by the BTUs per unit times the cost per unit divided by the efficiency of the device. 341300 is our constant (number of BTUs we consistently use as a measure of the heat generated).
So, for propane, we compute 341300 / 91500 * $2.10 / 1 to get the $8.91 shown above.
All of the BTU per unit figures are fixed, so only the cost of fuel and efficiency are changeable. Propane burned in a furnace that is 85% efficient would use more fuel to get the same amount of usable heat. More fuel equals more cost. We want to choose the lowest cost fuel and have the highest efficiency to spend the least on heating.
Now we come to electric heat pumps. They have an efficiency of more than one; they put out more heat than the electricity they use has available within it.
Since it is impossible to change the laws of physics, how do they do this? The answer is simple; heat pumps "pump" the heat from the air and move it indoors.
Understanding the concept is important to having a full idea of what works and what doesn't. First, the heat in air is nothing more than the movement of the molecules of the air, and the energy when they bump into something. If there is no movement of a molecule of air, it is at absolute zero, and has zero energy available for use.
Second, the amount of heat available depends both on the speed of movement of the individual molecule of air, but on the number of air molecules. You can get a little energy from one molecule, twice as much from two, and so on.
Once you have that concept down, the next concept is simply a neat trick known as Charles' Law. Remember using a bicycle pump? When you push down on the plunger of a bicycle pump, you compress the air into a smaller space, and thus raise the air pressure to the 32 PSI or 50PSI or whatever is needed to keep your bike tires inflated. At the same time, the bottom of the bicycle pump can get hot enough that you cannot hold it.
What has happened is that you have taken all the molecules that were in the air in the pump and compressed them into a smaller space. The heat (bumping of molecules) which was dispersed, is now contained in that smaller space as well. The molecules are closer together, so they bump more. The bumping is heat, so the bottom of the pump gets hot, or more simply, the temperature rises.
A heat pump uses this concept to grab the heat from the outside air, transfer it into a heat transfer medium (the refrigerant in the compressor and coils) and move it to the inside coil. The air going through the outside coil gets colder, and the air going through the inside coil gets warmer.
If the air outside is fairly warm, there is a lot of heat that can be harvested from it on each cycle of compression. Above 50 degrees Fahrenheit a heat pump can be as much as four times more efficient at heating than an electrical resistance heater.
If the air outside is cold, around 20 degrees or so, there is much less heat that can be harvested each cycle, so the air flowing through the inner coil cannot be heated as much.
What the designer of the heat pump system for your home has to do is take into account the average low temperature of your area, the heat loss through your walls and ceiling and windows (which increases the colder it gets outside), and the size of the heat pump. If properly figured, the heat pump he installs will have a balancing point where it can just barely supply enough compressed heat at the lowest common outside temperature in your area. That means at that temperature the unit will be running almost constantly and the air coming out of the system will be barely warmer than the air going into it.
What happens when the outside air gets colder than that or you want the interior at 75 degrees instead of 65 degrees? An auxiliary heater or furnace is automatically powered on by the thermostat, to help the heat pump get the air to the temperature set on the thermostat. That auxiliary heating source also gets powered on if you raise the temperature on the thermostat more than one or two degrees at a time. The manufacturer figures that if you are raising the temperature by three or more degrees, you want heat quickly, and that is more important than saving money, thus, the auxiliary heat will come on full blast.
In short, a heat pump works best when you least need it, works fine when the temperatures are above freezing, and degrades in performance quickly below that.
So how do you figure the efficiency and cost of running your heat pump? The short answer is that you can't. The efficiency varies so much that the best you can do (without some serious instrumentation and recording devices) is to make a guesstimate.
Even a guesstimate is important though, because you will be spending a large percentage of your heating dollars only on the coldest days of the winter. With that in mind, here is a reasonable guess of heat pump efficiency at various temperatures.
50 degrees F = Efficiency is 3
40 degrees F = Efficiency is 2
30 degrees F = Efficiency is 1.5
20 degrees F = Efficiency is 1
10 degrees F = Efficiency is .8
0 degrees F = Efficiency is .7
Why did I put efficiencies of less than one? According to the established tables, a heat pump should still be slightly over one in efficiency, even at 0 degrees F.. It may be, but the SYSTEM usually has losses.
Specifically, the energy used to power the fan on the outside is lost to heating. Even more importantly, the surface of the compressor or scroll gets very hot, and this too is outside, where the heat is lost. To make matters worse, a lot of air handler systems have ductwork that goes through unheated or minimally heated spaces, like in the crawlspace under a house. Heat leaks from these ducts, and the air at the end of a long duct may be colder than the air going into the system, even with the additional heat provided by the backup heat system. Additionally, heat pumps have a regular "defrost" cycle which turns the heat pump into an air-conditioner for a few minutes - to remove any frost that may have formed on the outside coil or valve and protect the equipment. Most units don't need to defrost anywhere near the number of times they do, but the user has no way of preventing these cycles.
All the losses combined means that at about 10 degrees F, it is likely better for you to set the thermostat on a heat pump down to about 55 degrees (or whatever is required to keep pipes from freezing overnight) and use space heaters or other heat sources to keep a small portion of the house warm.
If you want to save even more money, choose the coldest days as the days to do baking or to make stews that take a long time to cook, or to vacuum the rugs. All that energy will serve not only the original task, but as space heating as well. Got a cold dark day when the temperature is zero? Turn on your lights inside without fear of being wasteful! It will lessen the on-time for your heat pump and auxiliary heat and save money.
Remember that every system is different, prices of fuels and electricity can vary, and that ground source heat pumps do not degrade in performance the same way that air source heat pumps do. This is only a guide that you may want to tweak to match your own fuel costs and heating needs.
Some Sources:
Fuel Energy Content and Unit Conversion Tables
Heat Pumps
http://www.acdirect.com/new_faq/info...at_pumps_4.php (broken link)
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