## Thursday, July 6, 2017

### The Odd Insulation Math of US Department of Energy, Home Energy Scores

The following is public sharing of one persons' trial of US Department of Energy's Home Energy Scores Tool. The tool is a product of SRA International, Inc., in public ownership through US Government contract.

In a first post, I address access to the HES tool, and then finding of odd math of USDOE in dealing with a divide-by-zero problem in conversion of R-value to U-value, done stupidly as simply a number inversion of the insulation-only R-value. Energy is transmitted through resistances in addition to those of conduction through insulation and framing. The additional "surface" resistances are substantial and well known, though variable in every path. Where the savings achievable in any bid of weatherization must not be over-estimated, a highest value of surface resistance generally applicable, is wanted. In a derivation of Insulation Math , I offer that the wanted round number as a resistance value in USA units, is 3

Google search "u-value of an empty wood-frame wall "  finds this number affirmed by and by Build It Solar .

USDOE sets a wildly low surface resistances number, 0.4 without explanation. Perhaps such is possible for a shed with very-perforated walls. This might be in an odd very mild climate, else not habitable.

As insulation varies in effectiveness from full to worthless, energy waste changes in linear fashion in proportion to a Transmission Coefficient, U. A realistic particular situation must be considered to understand consequences of the USDOE error. Let that situation be a 2x4 @16 framed wall with at best R15 full filling of insulation .

With best insulation and correct usage of value 3 surface resistance, computed U-values are reasonably close, 0.063 my number vs. 0.087 by USDOE.  With worst insulation, none,
my U-value is 0.316, just a bit less than if a wispy wall had no framing thickness, U=1/3. At this condition the USDOE U-value is 2.28, over-estimating energy transmission and heating cost by a multiple of 7.2, roughly 3/0.4 = 7.5. Aside from other allowance by a Insulation Derate Tool, the wrong USDOE math will lead to excessive shaming of found conditions and to large over-estimate of weatherization benefits.  The whole USDOE process will fail to discover and report that perfect, fullest placement of insulation is absolutely required in weatherization. Perfect full-filling coverage is far more important than insulation depth or available thickness. The USDOE hire-an-interest-conflicted-auditor process will often lead to hiring of the auditor to pile more crummy insulation on top of a bad situation not repaired, doing more harm than good.

Content at this post will grow as I critically examine and try tools and the scoring process. Large errors found, will justify this examination.

Content for Home Energy Assessor Candidates is at
As I work in this online as a candidate, I am forced to employ a laptop computer with 64-bit OS and with unbearable difficulty of scrolling on the small screen. Offline I transfer lessons learned to my capable desktop computer running 32-bit but with large screen and other needed advantages. I must choose a 32-bit OS and hence 32-bit browsers with the desktop setup. I employ 32-bit to not give up important old software. HES training resources behave better on this full size desktop computer, employing the links that follow.

Primary Resources:

Introduction Video

Sim User's Manual
Here be sure to find critical information at Slide 6, not mentioned anywhere else:

"Driving" through a simulated house is not intuitive, and will be happily forgotten, irrelevant to life.

Step-By-Step Guide to Training House #1

Step-By-Step Guide to Training House #2

Home Energy Score Overview (Part II Study Guide)
Beware: This slide show contains the information needed to pass the final step in the assessor training, a twenty-question quiz. Read at Slide 2:
You will need to study this presentation to pass the Assessor written exam.
Print its 26 pages, and consult them as you sift through the multiple choices for each question. It isn't a "Part II Study Guide". It is the Multiple Choice Test answer key that you would surely have in hand if you have paid for assessor training.

Assessor Calculator
A URL for the calculator download is not offered. The online download is an Excel 2010 file usable only with Microsoft Office 2007 and newer. Such commercial offering is inconsistent with US Government policy. Here then is a free version of the calculator:

Secondary Resources:

Part 2: Roof, Attic & Foundation

Part 3: Walls

Part 4: Windows & Skylights

Part 5: HVAC & DHW Systems

Extra Resources:
Building Science

Remaining content is accessible only to those admitted to the beta web site.

3D Practical Training

House #1

House #2

House #3

3D Practical Test

Multiple Choice Test

User Review
(Submit feedback to SRA.)

Assessing The Assessor Calculator Tool:
The goal for existing home energy efficiency ratings shall be that anyone can find a score by himself if such has value, and with that believingly see how home improvements can move the score. Improvement is the need, not assignment of nonsense scores that do not motivate home improvements. There must not just be instead, an enrichment of cooperating organizations and auditors, in an absurd system. A home owner must find only self interest in the engagement with home-quality scoring mandates. We must not tolerate any involvement of persons not thinking first of the home owner interest.

Please see calculation as I perform it, superimposed on the insulation averaging portion of the HES calculator:

Applied math is evident in spreadsheet cell definitions:
For each of several parallel paths:
A pathway contribution of U-Value where all pathways add to 100% of path areas: This is simply (Fraction of Total) * (Path U-value). I can readily define as many parallel paths as are needed, typically four or more.

The HES Averaging Calculator imagines at most three parallel paths and poses for each a computed value UA, for example at Cell B30:
UA =B29/IF(B28=0,0.4,B28)

where B29 is a path's percentage of the total of all path areas, and B28 is the R-value of that path and has value not less than 0.4.

For this path in the first column at the Google Sheets link, HES computes 1.250 for a tiny piece of uninsulated drywall, an evil access hatch, and I correctly compute Ui = 0.005*0.333 = 0.00167, and 100*Ui = 0.167.

Average U-value, called "Cavity U-Factor," is simply the sum of values of (Fraction of Total) * (Path U-value). Instead, the tool poses a calculation such as:
B38 =(IF(B30=0,0,B30)+IF(B33=0,0,B33)+IF(B36=0,0,B36))/(IF(B30=0,0,B29)+IF(B33=0,0,B32)+IF(B36=0,0,B35))
computed by HES calculator for this path as U = 0.074, then inverted as R = 13.52.

For this attic floor with well-placed R19 batts, joist thermal shorts and, a little uninsulated hatch, I correctly compute U = 0.0519, then resolved as inverse minus 3, value R = 16.28.  At the next column, see that if the hatch is fully insulated R19, floor values change very little: U = 0.0504, R = 16.83.

We must counter false statements such as this of 1999, Don’t leave a hole in the ceiling ,  passed along by Habitat for Humanity, as written by southface.org:. It is way past time that the offending web page should be deleted or disconnected. Attic access is necessary, not evil. USDOE and Lawrence Berkeley Lab have not gotten the message. In wanting to demonstrate evil of a hatch if without an absurd stapled batt-on-top, the training considers a hatch 5% of floor area, perhaps of dimension 2 ft by 25 ft with a 1000 sf floor!

I wonder about behavior of complex if-statement HES calculator cell definitions that avoid a divide-by-zero problem. Examine this with study of a 2x4 wall that is well insulated with R16 batts, then with increasing decrepitude of the insulation batts as missing or not in contact with bypass:
Observe linear drop-off of value with decrepitude. Present again the tables at the top of this post:

There is not a razor's edge transition with "no insulation," but there are odd results if input no-insulation R-values in the HES calculator are less than 0.4. There is only an up to times seven error in U-value and energy cost with decrepit insulation (see discussion at top of post).

Now examine a crude provision for decrepit insulation in HES Calculator.
Here is a screen capture of the Excel form of the calculator, with function selectors in four tabs at bottom.

Where the Insulation De-rate Calculator is dysfunctional in the free version of the calculator, look instead for taught methods of USDOE perhaps mandated in Home Energy Scores, at an Insul-calcs tab now visible.

Here, defy an unfounded and outmoded bias for blown cellulose and against all batt insulation. Want well-placed insulation of highest quality as in filling a 2x4 wall to R15, regardless of insulation form . Completely filling the wall is what matters, then stilling bypass in convective loops.A rater may not be commanded to believe the HES calculator.

Assessment must allow  there is never instruction to give allowance for joist thermal shorts or for any decrepitude, as one might then do, shown here. In fact a subsequent step of derating insulation forbids direct allowances.

Fair and Poor installations may in fact have large areas without insulation contact, hidden from view and having no value. Regardless, the visually-interpreted table penalties are too small.