insulation and energy usage: understanding the practical significance of R-value

I’ve been quite focused on thermal gain/loss the last couple of years, as I started grappling with the reality of keeping a fiberglass travel trailer livable in a ‘four-season’ context, i.e. when it gets as cold as -10F at night, and more recently as I’ve been gradually outfitting a 8×12 cedar shed as an office and personal refuge.

Understanding what R-value actually means, in a practical sense, was difficult until I found the following formula, and started applying it to a known ability to generate heat:

R-value = (total surface area * (inside temperature – outside temperature)) / BTUs consumed

The R-value of a given structure can be estimated, averaged across the total surface area, by slightly modifying this formula:

BTUs required = (total surface area * (inside temperature – outside temperature)) / R-value

Here’s a good example:

total surface area = imagine the inside of the structure you’re heating as a 6-sided box. Add up the square footage of all six sides of this box, since heat generated will radiate out all sides: ceiling, floor, and walls + windows + doors. In the case of my 17′ fiberglass travel trailer, this is a minimum of 423 sq. ft.

temperature delta = I want to keep the average temperature at the walls at 55F; actual air temperature ends up being 5-10F warmer than this, so reasonably comfortable with an extra layer of clothing. The outside temperature for this example will be 32F. This gives us the temperature delta of 55F – 32F = 23F

BTUs consumed = through observation and experiment, I’ve learned that I need to run a 1000w mica panel heater at near maximum thermostat setting, so let’s say it’s going to be on 90% of the night at the coldest point, to maintain a 23F temperature delta. Multiply watts by 3.4 to get BTUs, then add approximately 200 BTUs for a sleeping adult, since I am adding a small amount to heating the total space when I’m in it. So, we have ((1000w * 90%) * 3.4) + 200 = 3260 BTUs

Now, we’ll plug these numbers into the formula to find out what the average R-value of the inside of my trailer is:

(423 sq. ft. * 23F) / 3260 BTUs = R 2.98

Chances are I have a better R-value than that, overall, because the inside of the trailer is a fairly complex surface, with cabinetry, benches, and so forth presenting a much greater total surface area than just flat surfaces. The 423 sq. ft. is a conservative estimate generated by treating the inside of the trailer as if it was an empty box. The entire floor and area underneath the bed platform is covered with a close-fitted 1-inch thick layer of XPS hard foam (R5), and then a half inch of neoprene mat on top of that, for a total of around R6.5 on the floors. The walls are rated R5, and any area covered by cabinetry might get a slight bump from the added bulk. On the other hand, experiments with a infrared thermometer to guage heat loss winter before last showed that the wheel wells and area around the fridge’s external access and venting is close to R1, and thus prime candidates for some fine-tuning of insulation in nooks and crannies.

When I’m out and about in off-grid mode, I have a maximum of 9400 BTUs of heating available, 9200 from the 12000 BTU propane furnace, and 200 from me. The other 2800 BTUs from the furnace ends up waste heat going out the furnace exhaust, which is kind of a shame. So, if I wanted, I could even use the formula to figure out the coldest possible outside temperature at which this amount of heat generation could keep me comfortable. Let’s also pick a somewhat more reasonable number for surface area, since I clearly have an average R-value close to R5 than R3. So, we’ll estimate 700 sq. ft. of total surface area to be heated, with the corresponding adjustment to R-value.

9400 BTUs / (700 sq. ft. / R 4.93) = 66F

So, I know that the maximum cold temperature I can handle with this combo of R-value and heat generation capability is 55F – 66F = -11F

Just for fun, and because I’ve actually used the technique, we can add in a small gas-powered generator (a Champion 73536i, rated at 1700w running), running the mica panel heater at its low 500w setting. This allows the generator to be run in ‘eco’ mode, and lets me stretch a gallon of gas 7-8 hours. The bonus is that this configuration, with the generator 120v output run into the trailer’s 30A electrical system, provides a healthy supplemental charge to the two deep-cycle batteries in my setup.

500w * 3.4 = 1700 BTUs

1700 BTUs + 9400 BTUs = 11,100 BTUs

11,100 BTUs / (700 sq. ft. / R 4.93) = 78F

Now, I have the ability to deal with temperatures down to -23F. The main drawback is that the supplemental 1700 BTUs come at a very high price, as the gallon of gas will effectively double my heating costs for that night, making gas about 5.5x more expensive than propane for this application.

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