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The mathematics of home heating

As the winter comes on, fuel costs are once again on people's minds. Alternatives to cut those costs are few and far between, but there are choices out there. We're going to look at the arithmetic with which we compare them.

Fuel cost comparisons drive my students crazy, but they are based on simple comparisons. I do them this way: How many BTUs can a penny buy. There are other ways to compare them, but this is as good as any. First let's look at the units by which we buy energy, which is what BTUs (British Thermal Units) are.

The common energy sources are natural gas (methane and some miscellaneous and minor other gases mixed in), liquid petroleum gas (LP, or propane), fuel oil (usually number 2), and electricity. Their units are as follows: methane, purchased mostly by the cubic foot; LP, purchased always by the gallon; fuel oil, also by the gallon, and electricity, by the kilowatt, or KW.

Natural gas retailers have muddied up the situation by using different units of energy. One supplier may sell you MCFs, which is the Roman numeral "M." That stands for a thousand, or a thousand cubic feet of natural gas. CF stands for cubic feet. Another supplier may sell a unit to you called a therm. That means 100,000 BTUs. Since one cubic foot of natural gas has a thousand BTUs, a therm is 100 cubic feet. There is yet another unit of natural gas, called a decatherm, or 10 therms. And yet another: The CCF, or, since that's the Roman number C, which is 100, this is 100 cubic feet, which is another company's therm. Why these suppliers do this isn't clear, but then, one might hypothesize that they don't want to be clear. Then, since this natural gas comes out of the ground and varies in strength, they use multipliers to compensate. (Ah, boy. I am such a suspicious guy.) I once called a supplier to ask what all these multipliers were on a customer's bill, and had to get three different people before they could explain what various multipliers were used at various times during the month. Being an energy supplier means never being too clear about costs.

Some bills that I have looked at have no unit designation on them at all; it is up to the customer to decipher exactly how much is being paid, and what units are being used.

So much for natural gas. LP is sold by the gallon. Each gallon contains 92,500 BTUs of energy. Pretty straight forward of them, really.

Fuel oil is also sold by the gallon, and most people buy number 2 fuel oil, which has 140,000 BTUs in each gallon.

Finally, electricity is always sold by the Kilowatt, or KW. One KW has approximately 3,400 BTUs in it, which is simple, until one begins to dig into the alternative peak vs. off-peak pricing that the manufacturers of it have provided. Which is good. Good for us, and good for them. It's good for them because they have a big problem with their generation of it. People get up in the morning, take showers, turn on lights, coffee pots, electric cook stoves, turn up various forms of electrical heat (or cooling in the summer), and in general make the electricity providers' lives one continual hell of guess work as to how much they have to provide each second.

Midmorning comes, everyone shuts everything off, and now there is too much excess capacity on the grid. Once again, hell. So they figure, instead of keeping extra generators spinning and wasting coal or whatever energy they're using to keep them spinning so they can bring them on line promptly and prevent brown outs, they'll offer a cheaper rate, which you'll like. The cheaper rate comes with a downside: They can turn you off at these hours of "peak" consumption, which makes their life easier. So off-peak electricity is cheaper.

Here's how they compare. Off-peak electricity for heating, if you spend the money to get wired up for it, goes locally (I've checked with Otter Tail Power and Lake Region Electric) in the 3.4 cents (Otter Tail) or 5.4 cents (Lake Region) per KW, or 3,400 BTUs, which comes out around 1,000 BTUs (Otter Tail), or 630 BTUs (Lake Region) for a cent. And since it's 100 percent efficient for you -- no chimney loss -- you get it all.

LP is about $1.80 per gallon, or 180 cents. Divide 92,500 BTUs in a gallon by 180 cents, and you get 513 BTUs for a cent. But wait: Your new gas furnace is 92 percent efficient, so we still have to multiply 513 by .92, so you only keep 470 BTUs.

Fuel oil, number 2, is around $2.60, or 260 pennies, and a gallon of it has 140,000 BTUs. Divide 140,000 by 260 and you get 538 BTUs for a cent, except your oil furnace is only 80 percent efficient. So multiply times .80, and you get 430 BTUs.

Natural gas in Wadena, Perham, Fergus Falls, and most of the Midwest is hovering around $7 for an MCF, (1,000 cubic feet, with a thousand BTUs in each cubic foot. I've deciphered each of these town's bills individually, and although they each sell by different units, I have converted them all to MCF.) So divide 1,000,000 BTUs in an MCF by 700 pennies, multiply that times .92 percent efficiency, and you have about 1300 BTUs for your penny. New York Mills is an exception (There may be others, but none that I am aware of), with natural gas over $12 an MCF, depending upon quantity. You can do the math.

But off-peak electricity is winning right now, out in the country, no doubt about it. You have to have a back-up source of heat, so if they shut you off you won't freeze, and you're going to have to invest some money in it, but if you're in a category where this looks good, check it out and get some bids. Pay back is pretty easily calculated.

Electricity has more variables that haven't been considered here, with heat pumps, both air and geothermal, complicating things. Maybe next time.