I live in a region which is heating-challenged. Every house or apartment I've lived in has had issues with heating in the winter and cooling in the summer. Builders in this area just don't seem to get that a little insulation goes a long way. For my current house, the homeowner's association also decided in its infinite wisdom that it would rip out all the old oil-fired boilers because they were too expensive, and replace them with electric baseboard heaters, because they are more economical. Whatever insane reasoning that led to that decision is now negated, especially since electricity has doubled in price over the past two years here. While it is true that electric heaters themselves are 100% efficient, the power plant and transmission lines are not. Furthermore, baseboard heaters tend to be mounted on outer walls below windows, so much of the heat can be conducted through the wall and escape the house.
I'm trying a few new strategies to try to make my house more comfortable, given its current limitations. First, I added transparent window films to almost all of the windows. The idea is that they hold an still pocket of air against the window, which adds an extra insulation factor. They also can contain small drafts so that cold air can't get in. It does take some work to install them, which basically involves stretching a huge sheet of saran wrap onto double stick tape mounted on each window frame, but eventually I developed a pretty efficient method (especially for smoothing the wrinkles).
A second thing I did was install curtains in the living room doorways, in order to keep the heat from escaping to colder parts of the house from the room I use most. These are cheap but heavy curtains I got on sale at Wal-Mart, hung from an expandable shower curtain rod across two doorways. Finally, I put some foam-board over my back door. It's a thin wooden door that conducts a lot of heat out.
I think these efforts have helped in a very qualitative sense. The living room is much less drafty, especially near the windows. Before installing the films, a cold down-draft from the windows would collide from an up-draft from the heaters to make chilly turbulent zone right where I was sitting. These drafts are gone now. The curtains also definitely help keep the heat where I appreciate it most.
Comfort is good, but I'd also like to know if this is saving energy and money.
PEPCO kindly puts my energy usage history on each bill, so it was a matter of collecting a few old bills and entering them in the computer. That's shown in black below (click for larger image).
The plot shows the number of kiloWatt-hours I use each month (ignore the red and blue curves for the moment). Unfortunately, I don't have data yet for December, the first month that I installed the window films or curtains, so I have to put the efficiency question on hold for now.
I decided to check out this plot a little more carefully. I use the greatest energy in the winter, obviously for heating. There are also small bumps in the summer, corresponding to cooling. Up until recently, I had a very old air conditioner which I rarely used, so my cooling expenses have never been large.
What to compare this with? Well, the there is a nifty number called a heating degree day used for heating calculations. Basically, any day that the mean temperature dips below 65 degrees Fahrenheit is considered a "heating day," and for that matter when the mean temperature is above 65 it is a "cooling day." The number of heating degree days is the number of degrees the mean temperature is below 65. The US National Climatic Data Center (not to be confused with the Climactic Data Center! Ooo la lah!) provides tabulated historical heating and cooling degree day data. The monthly total heating and cooling degree days are shown in the above plot (red=heating; blue=cooling; averaged over Maryland & Washington DC).
It's no big surprise that the heating and cooling curves match up with my energy usage pretty well. It's physics after all.
In fact, the Mr. Quantitative in me wants to do more. I decided to perform a linear regression between these quantities, with energy usage per day as the dependent variable, and heating/cooling degree days per day as the two independent variables. The simple function I tried was:
E = Constant + H(Th) + C(Tc)
where H(Th) is some function of heating degree days (per day), and C(Tc) is another function of cooling degree days (per day), both of which describe power usage versus temperature. This equation has the interpretation that I use some constant electric power all the time (for lights, water heater, etc.), plus the amount I use for heating and cooling, which depend on temperature.
The obvious choice is to make the two electric heating functions, H and C, proportional to temperature. However, I found that wasn't a good fit, as you will see below. Instead, there is an activation threshold. For small temperature excursions, no heating or cooling is required, and I don't use energy. This would be my comfort zone, the temperature range I'm willing to tolerate. I imagine I have a larger comfort zone than many people. As the outside temperature gets more extreme, then I use energy to maintain the inside house temperature within the comfort range. This function can be written as a constant when the heating/cooling temperature is within the comfort threshold, and a linear function outside of that. The linear coefficient of the function describes the number of kiloWatt-hours per day needed to heat (or cool) the house one extra degree Fahrenheit.
The fit works quite well, and here is how the results look. On the heating side, the function H(T) looks like this:
This means that I am willing to tolerate mean outside temperature drops of about 6.5 degrees (F) below the baseline temperature of 65 degrees before turning on the heat, and then I use about 0.84 kWh of energy per day for each degree (F) that it gets colder. At the current PEPCO price of 10.96 cents/per kWh, I pay an extra 10 cents per day for each degree colder that the outside temperature goes below about 59 degrees.
On the cooling side, the curve looks like this:
I'm apparently willing to tolerate large excursions before turning on the air conditioner (up to 10 degrees above the 65 degree baseline), and then I use 1.31 kWh of energy per day for each degree above that (for a cost of about 14 cents per day for each degree).
Finally, it's worth noting that I use 9.7 kWh of energy every day, no matter what the outside temperature is, just keeping the house going. I know for a fact that my refrigerator uses about 3.8 kWh every day on average, or about 40% of the total. It's a very old refrigerator from 1982 (!) which needs to be replaced. I used my handy Kill-a-Watt energy meter to measure this and other devices in the house. The refrigerator is by far the largest constant energy user.
Interestingly, last winter I changed from incandescent and halogen lamps to compact fluorescent bulbs. I predict this should save me between 1-2 kWh per day. A change such as this is barely detectable on the graphs, given the season and monthly fluctuations.
As one final exercise, I can estimate the overall efficiency my house, the effective "R-value". This quantity is defined as the reciprocal of the amount of heat lost per unit time per exposed area per degree temperature change, and has units of ft2 per (BTU/hour/Fahrenheit). I already know the second quantity, since it's the linear heating coefficient I found above (0.845 kWh/day/F = 120 BTU/hour/F). The exposed area of my house is about 2000 ft2, giving an effective R-value of 17. (NOTE 14 Jan: my original value of R-0.7 was had a unit conversion error and was incorrect).
An overall insulation efficiency of R-17 is okay but not great. As pointed out here, a house in my region (zone 2) demands an R value in the range of 18 (walls) to 49 (attic). However, as one of my commenters notes, there are other factors to consider, like how much air circulates through the building.
Remember that this data is all based on my house before I made the few changes above. Neither my usage data nor the climate data for the winter heating season are available yet. I hope to see improved efficiency!
Update (14 Jan): Oops! I made a unit error when converting from kWh/day to BTU/hr (missed a factor of 24). After the correction, the overall insulation efficiency of R-17 is more reasonable.
15 comments:
Reading through your article I got many great ideas which I`ll imply at home. I`m afraid I would still have some problems knowing the improbability of heating up properly the Toronto houses. We went through the oil-fired boilers which proved to be useless but the electric baseboard heaters are quite efficient leaving out of consideration the electricity bill. Anyway, thanks for sharing your ideas with us!
Dude, that house was built before they knew what a BTU was! R = 0.7! Maybe you're underestimating the area the heat is flowing through? Even so, it's maybe not too surprising. Do the walls have any fiberglass insulation in them? You need to blow some urea-formaldahyde into your attic. You know where urea comes from, right? Either that, or knit a really big sock and just put the whole house in it. nice post.
Oh, and I almost forgot, nice
feng shui curtains!
@tod, I know that when the home-owner associated refurbished the houses a few years back, they blew "insulation" into the walls. I say "insulation" in quotation marks, because a neighbor told me that when she opened up a wall for some repair work, she found the insulation was a solid lump collected at the bottom. In other words, there was no insulation value at all!
I'm concerned that I made a numerical mistake, but the math is simple enough. The area I used includes all exterior walls and roofs, and also the floors, but excludes my adjoining neighbors.
Hey man this is Sarah and I'm just saying u have way too much time on ur hands!!! Nice curtains and I had no idea u shopped at walmart!
Sarah S.
@Sarah, thanks for the comment! Looking at the data was easy and fast. It took a lot longer to write it up...
I shop at Walmart when I'm looking for cheap curtains, that's for sure! Oh, and when I need to stock up on more Faded Glory jeans.
I think I might have spotted an error in your calculation. Basically there are two main components to the heat required to heat a house:
1. The heat loss through the material of the walls, roof, floor, windows, and doors.
2. The heat loss through ventilation: basically your heating system heats the air, and some of that air escapes to the outside (you need some level of ventilation to breath, so this is essential).
Energy consultants usually calculate the ventilation part of the heat loss by assuming an air change rate: air changes per hour. Of the top of my head I'm not sure what would be normal for a house but maybe one or two air changes per hour. So basically all the warm air in the house gets changed with outside air something like twice in one hour.
These air changes account for a big proportion of the energy consumption required to heat the house - quite likely 50% or more, especially if your house is draughty.
Actually, although calculating steady-state kW heat loss (when the house is already warm) is fairly effective (you basically work out the R, or U, values of all the walls, floor, roof etc., estimate the air changes per hour, and work out the steady-state heat loss at any particular outside temperature), estimating the actual energy consumption from R values and air changes per hour is much more tricky. This is mainly because of intermittent heating. Basically calculations start getting really complicated when you consider the energy required to heat a house up after it's cooled down below it's comfort temperature (e.g. overnight, or when you're away). Thermal admittance comes into it, and calculations of energy consumption tend to come out way off the mark...
So, for these reasons, I'm not sure you'll ever get an accurate idea of your overall R value by working backwards from your energy consumption!
Incidentally, there's more information on correlating energy consumption with degree days in this article on degree days. The linear regression you did is actually something energy consultants do quite a lot.
@Martin, thanks! If what you say is true, then the quality of the insulation is less important than the air circulation rate. Unfortunately, I think my house actually is quite poorly insulated, which is hurting the efficiency. I also think that because the baseboard heaters are mounted on exterior walls, much of the heat is being directly conducted to the outside. I wish they had installed insulating stand-offs so that the heater boxes weren't mounted flush to the wall. (I live in a housing cooperative, so I don't exactly have control over these things).
In any case, by putting up window films, I should have blocked some of the sources of draft, and increased the insulation quality, so it will be interesting to see if my energy usage did indeed go down.
If your windows were draughty then the window films will probably make a pretty big difference. It'll make a difference to the U-value anyway, but, if it blocks draughts, the benefit will be quite a lot more than the benefit from improved U-value alone. Of course exactly how much depends on how big the draughts were, and how big the windows are...
Improved insulation would likely make a big difference too, but, for draughty buildings, blocking the draughts is often the quickest and cheapest way to make some pretty big savings by bringing that air change rate down.
You can probably also get some cheap draft exclusion tape stuff to go around outside doors - it works well too.
Note that I found an error in my calculations, and the post has been corrected. The comments above were responding to the original (erroneous) insulation value of R-0.7, and not the corrected value of R-17.
so ... you gonna update with data from your little improvements?
I'm not sure that the definition of 'cooling degree day' uses the same baseline of 65 degrees. No one cools their homes that much on a hot day. What if you used a base of 75 degrees?
I know this is an old post, but I stumbled upon it. I'm a consultant for sustainable building and I appreciate your investigation of your own energy profiles in and around your house.
I just wanted to add that you are probably making a large mistake somewhere to calculate your Rc values of your walls and roof. A typical Rc value for a well insulated modern newly built house is around 3.5, in Europe. Older houses typically don't come above 1.0, even with insulation added.
Also, indeed ventilation (also through cracks) is a major source of energy loss in a house. Therefore, modern houses are buolt very tight, and have heat exchangers to recover the energy from the exhaust air.
cheers, Tom
@Tom, thanks for your comment. Surely your European insulation value is based on metric units. The value I quoted was in (crazy) imperial units, as I noted in the post. An imperial R-17 insulation value is still very modest.
Yes, that might very well be the case, itwould then be divided roughly by 9, correct? Being R-17 imperial is about 1.9 metric?
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