[bialpio]

Naive question: is reduction in energy loss linear with R-value or is there a different relationship? Improvement of R-value by 35% tells me nothing if the function to calculate energy loss does something strange with the R-value afterwards... :)

[mikeyouse]

So R-Value refers to the material's ability to resist heat flux and depends on the temperature difference between either side of the assembly. The general formula is Heat Loss = (surface area x temperature difference) / R-Value

So as you rightly hypothesize, the "first" bit of insulation is more important than the next bit. Going from R-1 to R-2 decreases energy loss by 50%, going from R-2 to R-3 decreases it by a further 30%, R-3 to R-4 by a further 20%, etc.

So for my example with a 40ºF difference between inside and outside, if that wall assembly were 120sq ft, the original wall with R-6.15 would be losing 780btu/hr. The 13% improvement in R-Value from the first example would reduce energy costs by 10% (700btu/hr of energy loss), the 35% improvement would reduce costs by 25% (578btu/hr). It's strictly better to increase r-value but the highest leverage impacts come from the bottom.

[waldothedog]

I believe Ufactor is a more holistic/thoughtful figure for thinking about energy transmission through building envelopes. Might be of interest

https://www.greenbuildingadvisor.com/article/all-about-u-fac...

[mikeyouse]

In a sense that's true - it's more natural to consider in the same way that MPG is less obvious compared to gallons per hundred miles. But they're representing the same quality, U-Factor is just the reciprocal of R-Value.

So R-Value represents the thermal resistance and U-Value the transmittance but you can easily take the reciprocal of one to get the other (e.g. my R-2 window is just a U-0.5).

[bialpio]

First off, thanks for the explanation in your other post! The main point I had is that there are gotchas when talking about improvements in R-value in terms of percentages that we the uninitiated won't be aware of. U-value doesn't seem to have that problem if it's just a simple reciprocal of R-value (IIUC, halving U-value halves heat loss, doubling it doubles the heat loss - that's a way easier relationship to understand to me).

[mikeyouse]

Yep, that's a good point and a good way to think about it.

My MPG reference was an eye-opening moment for me -- the US uses MPG which is really backwards from what you care about (in the same way that R-value and U-value are). So increasing your mileage from 10mpg to 12mpg saves exactly as much gasoline as increasing your mileage from 30mpg to 60mpg. This is plainly obvious when you consider gallons per 100 miles, [10->8.3] & [3.3->1.7].