Measuring your house walls R-value with an infrared thermometer
Using an infrared thermometer, I devised a way to measure the insulation R-value of the outside walls of the house.
On a cold day, when the outside temperature was -15°C, I measured the wall temperature of our bedroom at 13.3°C, and a dresser near the same wall at 14.8°C. We like to keep the bedrooms at a cool temperature.
Assuming the dresser is at the room's ambient temperature, the 1.5° temperature difference is taken up by the insulation properties of the air boundary layer to the wall. This is assuming all temperatures are at steady state, and that the sun isn't shining on either side of the wall.
The effective R value of the wall surface, at a 1.5 degree temperature difference is R 0.728 (or Rsi of 0.13). R-value is measured in BTU per square foot per degree (F) heat transfer, whereas Rsi is Watts per square meter per degree Celsius. To convert Rsi to R(imperial), Multiply Rsi by 5.8.
Given a 28.3 degree temperature difference to the outside, and knowing that heat transfer is temperature difference over R value, and that the amount of heat transfered through the wall is the same as the heat transfer across the surface, we can write the equation:
From this, we can solve for Runknown = R0.738 * 28.3° / 1.5° = 13.9
Which works out very close to the expected value because the walls of the house have 3 5/8" of fiberglass insulation between the 2x4s. But there is also 3/4" of wood sheathing on the outside, plus a 1 1/4" air gap, and 3.5" of bricks. Each of these adds a little to the insulation, which I assume accounts for the difference between the expected R12 for the fiberglass and the measured R13.9
This all relies on being able to measure the surface temperature fairly accurately, and these relatively cheap infrared thermometer are a limiting factor. The one at left is one I bought quite cheaply for $20 Canadian. I found that one a bit inaccurate, especially if the battery gets low, or the temperature of the thermometer itself varies too much. The one at right cost $40 Canadian ordered on line and works much better.
For relative measurements, the absolute accuracy doesn't matter that much. But I found when measuring temperatures just a degree or so apart, the thermometers didn't realize a new measurement was being taken and just kept averaging with the previous reading. To get around this, it's best to measure something very different in temperature between readings, such as the surface of my hands.
It also helps to go back and forth and repeat the measurements a few times, just to make sure the number you have is representative. Being off by 0.2 degrees in this case would change the result by 15%.
I made a spreadsheet for calculating the R-value of the boundary layer based on temperature difference. Then, to save you some algebra, I also included columns of the calculated wall R-value based on the temperature difference to the outside.
There is also a column for heat loss, measured in watts per square meter of wall, which allows you to calculate the rate of heat loss through the walls of your house.
Please note that the version of the spreadsheet used in the video had an error in the formula for the column for heat loss (W/m2). The version here is fixed. Fortunately, that number wasn't used for the R-value calculations.
I looked up "thermal radiation" on Wikipedia. The slope of this graph doesn't change much between freezing and body temperature, so I drew a red line roughly parallel, and measured it's slope. The line rises by 1000 watts/m2 over a temperature range from 225 to 400°Kelvin. 1000 watts divided by (400-225) = 5.7 watts/m2°C.
The other component of surface heat transfer is heat conduction to the air, assuming there is no wind. Warming or cooling the air causes convection, which in turn increases the rate of heat transfer, which means the heat transfer rate increases faster than temperature. I used the formula for "vertical surface" at left, from this document and plugged that into the spreadsheet.
I then added the two conductances as a function of temperature and calculated the inverse of conductance to get thermal resistance, Rsi (in metric). Multiplying Rsi by 5.8 converts it to R-values for imperial units. The imperial units are useful for comparing insulation, as most insulation here (in Canada and in the US) is rated in imperial R-values. But Metric Rsi values are much more useful for calculating heat loss, unless you like to suffer and perform thermodynamics in imperial units. When I took thermodynamics, we had to learn to do it in both systems of measurements, and we not allowed to just convert to Metric, do the calculation, and convert back, because that would have been easier than calculating thermodynamics in imperial units.
Hot water insulation blankets worthwhile?I ended up using that same spreadsheet again to calculate the heat loss through the walls of our hot water heater and evaluate whether one of those insulating blankets is worthwhile. IN the case of the blanket I bought, definitely not worthwhile, but if you can get a better insulating blanket for less, it can be worthwhile.
Please note that the "W/m2" column of my spreadsheet had an error in the formula, which ended up throwing my energy calculation off by 20%. The actual savings are 20% higher.
If you get a better insulating blanket, pay less for it, and your electricity costs are higher (electricity is relatively cheap here), the payback period could end up less than one year.
Building an air raid siren
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