Low Technology Institute

Last year I built prototype solar panels and summarized the preliminary data gathered in some test runs (see this project’s archive here). I’ve been collecting performance data over the last year and am now ready to present the results.

Data Collection

The data for this analysis comes from three temperature loggers (Elitech RC-4, P.S., we do take donations from our wish list). The loggers’ temperature sensors were placed in three locations. The first is in the hot-water reservoir, where the heat of the day is stored and transferred to our household hot water. The second is on the pipe leading out from the reservoir to the panels. The third is on the pipe coming back in from the panels to the reservoir. The difference in temperature between the last two gives us the temperature rise that the panel produces.

Oops, Check Your Data Recorders

When I went to download the data from the temperature recorders, I was in for a surprise. They hold 16,000 data points, but because I set them to record every 10 minutes, they ran out of space after less than four months. The data collection started in mid-November and ran through the beginning of March. This represents the coldest and least-sunny part of the year. This means that the BTUs and other performance discussed below is not representative of a full year.

The Data

Below you can see the raw data. It includes the data serial number, date and time stamp, and the temperatures (in Fahrenheit) of the reservoir, pipe in, and pipe out.

But this is not really human-digestable information.

Even in graph form, it is a little much. The sharp red spikes are the few hours each day when the sun was shining on the panels; usually between 10:00 a.m. and 3:00 p.m. We had a few spikes in mid-November and the end of January when I was monkeying with the pump. The water in the panels was stopped for a little while and got hotter than usual.

The downward red spikes show that the panel is turning on before the water in the panel is fully hot, meaning I might need to adjust the PV panel that powers the system pump. On the other hand, it only takes about 20 minutes for the cold spike to dissipate. I’ll wait until I have a full year’s data to make any adjustments.

The blue spikes are telling us something important, too. The water out of the reservoir is always as cold or colder than the reservoir temperature (the black line). This means that all the heat created by the panels is getting stored (the hot water flows through 100 ft of copper coils inside the reservoir; otherwise known as a heat exchange). If we saw the blue line spiking above the black one, we’d know that my heat exchanger wasn’t doing its job.

“Year 1” Stats

I’ve cleaned up the data and compiled a more user-friendly dataset. Essentially this shows the day-by-day rise in the reservoir temperature. If the system was not running due to cloudy conditions, it was simply marked as 0°F.

As the system holds 500 gallons of water, we can compute the BTUs collected by the panel: one BTU is what it takes to raise a pound of water 1°F. Therefore, each degree of temperature rise is 4150 BTUs (500 gal. × 8.3 lb/gal = 4150 lb). The first panel built measures 4 × 16 ft, for a total of 64 ft². If we divide the total BTUs produced in a day by the panel area, it gives us our BTU/ft²/day for the panels.

The day’s weather conditions are the driving factor for panel performance. I collected the daily high temperature as well as overall weather conditions (sunny, mostly sunny, mostly cloudy, and cloudy) from the Dane County Regional Airport.

These data can be represented graphically, although I got a little carried away and maybe overcrowded this graph. The red bars correspond to degrees of temperature rise in the reservoir as well as BTUs produced (left scale). The black line represents the high temperature outside for each day (right scale). The shaded backgrounds represent how sunny or cloudy it was on each day.

I want to point out a key thing this graph tells me. Outdoor temperatures do not drive my solar hot water system, rather the amount of sunshine. This may seem obvious, but the real proof came at the end of January, when the high never made it above -10°F, but the system still produced almost 500 BTUs/ft².

Extrapolating from the Data

Although we only have the BTU output from the least sunny months of the year, we can get an idea of what to expect in the summer months. Using an insolation calculator (such as this one), we know that in December, 2.87 kWh falls on a square meter in a day on panels with a 47° tilt. July, on the other hand, produces 5.36 kWh/m²/day. By compiling the insolation (amount of solar radiation) rates for our location over the year, we can estimate our monthly BTU output by multiplying our sunny day BTU production by total number of sunny days per month. We will see how closely this estimation bears out.

Month | Insolation | Observed | Sunny Days | Estimated
      | kWh/m²/day | BTU/ft²/d|            | BTU/ft²/month
Jan   | 3.25       | 436.8    | 13         |  6,262.9
Feb   | 3.81       | 576.5    | 13         |  7,303.3
Mar   | 4.21       |          | 13         |  8,046.3
Apr   | 4.58       |          | 14         |  9,405.5
May   | 4.86       |          | 16         | 11,389.3
Jun   | 5.20       |          | 17         | 12,927.3
Jul   | 5.36       |          | 19         | 14,882.4
Aug   | 5.05       |          | 19         | 14,040.7
Sep   | 4.85       |          | 17         | 12,076.9
Oct   | 4.12       |          | 16         |  9,697.4
Nov   | 2.94       | 483.9    | 11         |  4,812.1
Dec   | 2.87       | 427.5    | 12         |  5,129.6

For those really interested in this extrapolation, here’s how I did it. I calculated the average BTU/ft²/day for each full or partly sunny day in each month (monthly total divided by sunny day) and put this in the “observed” column. I then ran a regression analysis on the insolation vs. observed data. I got the formula f(x)=142.9x + 17.34. The R² for this was only 0.71, but with such few data points, this is expected (the linear regression was closest, but I also tried exponential, logarithmic, and power regressions). I then plugged the insolation rate into the formula to calculate the estimated BTU/ft²/day per sunny day and multiplied this by the number of sunny days per month to calculate the estimated BTU/ft²/month.

“Lab Notes” are a series of posts chronicling the daily progress our research projects. Research Project No. 1 is the testing and installation of a solar heating system for domestic water and space heating. These notes may be useful for anyone interested in building such a system at home. Others might prefer the more succinct guide to solar heating, videos, and other formal publications that will result from this research project and be posted to the website as they are available.