Flawed Measurement Of R-Value With A Certainteed InsulSafe4 Gage

I want to at last dispose a gage saved from a job in which I concluded the following:
The Builders Statement of found insulation states that for intended R38, one bag covers 44 sq ft. 37 bags were applied, sufficient for 1628 sq ft. The installer was unaware of actual area  2315 sq ft, then with 30% under-fill,  R26 before discount for overwhelming consequences of missing insulation.

General fill of insulation was 10", not a goal of about 15".  A greater depth of insulation did not exist at time of construction, then lost by settling. A failure of inspection occurred, on top of a perhaps-conscious failure of math. Was compensation for the job not proportional to cost of materials?

Adjacent to the found access hole where inspection would be expected, the gage is revealed at 10" depth. By human nature, depth is less at a majority of area not accessible for inspection.

Here is a cropped photo of the gage, with marking of depths at values of common interest, a black line and arrow under-lining each named value.  For example, named value R60 is at depth 22.0".The gage corresponds to a table in PDF document InsulSafe® SP Installation Guide - CertainTeed .

Having insulation generally R26 where R38 was wanted, is mean. Call the weighted average of loose fill R24.  The overall effective R value of the attic floor is diminished by areas bare of insulation and by thermal equalization of interior walls through assorted floor openings often large. Bare areas are mainly at edges of the attic, and are typically 5% of floor area.

Do the Insulation Math , of found effective R-value:

Allow for thermal shorts of 2x8@24" framing.

1/(R_eff + 3) = f_joists/(R_joists +3) + f_{insulation in contact}/(R_insulation +3) + f_bare/3

For 2x8 framing, R_joists is  6.8.

1/(R_eff + 3) = 0.06/9.8 + .89/27 + .05/3

R_eff = 15

The work of sealing the attic floor is an insulation cost, and I think the expenditure should be encouraged by allowing its result is that of finding another 5% floor bare area:

1/(R_eff + 3) = f_joists/(R_joists +3) + f_{insulation in contact}/(R_insulation +3) + f_bare/3

1/(R_eff + 3) = 0.06/9.8 + .84/27 + .10/3

Found attic floor insulation:

R_eff = 11

The now-accessible attic has a large decked area 18.6" up from ceiling drywall, and much additional area accessible with movable flooring upon raised floor supports. HVAC ducts are more efficient and are buried under floor insulation where allowed. Conditioned space below the attic floor is 2315 sq ft.

A section of hallway ceiling ruined by step-though during electronics wiring is now occupied by a wonderful European attic ladder.

Ladder installation at a 45° diagonal across 2x8 floor joists is supported by 2x18 box beams, a first-ever feat of cleverness.

I imagine a 150 sq ft work room 8' tall from the new flooring level, at the attic space with greatest headroom. The space might be a wood shop or music room, conditioned or not. An attic has congenial temperature a portion of most days of the year.

With dispersed insulation,  f_bare is zero. One bag of R21 insulation, 89 sq ft, 89/2315 = 4% of the floor, is placed over the master bedroom loft ceiling. 5% of the floor at eaves is insulated to R30 with pushed loose fill. The remaining loose fill is 3" to 4" deep everywhere else, called R11.

1/(R_eff + 3) = 0.06/9.8 + .04/24 + .05/33 + 0.85/14

In the now-accessible attic:

R_eff = 11.

This is the same as-found, not diminished. Where this condition must exist for some time, my churn of insulation beyond just creating safe attic access, has not hurt my customer. This finding is very important to me. I hope you agree with my math. Distributing insulation to eliminate bare areas is smart, even where found unstable loose fill insulation is collapsed in the churning.

Find then:
Perfect, fullest placement of insulation is absolutely required in weatherization. Perfect full-filling coverage is far more important than insulation depth or available thickness. Where insulation has been placed carelessly, do not hesitate to trample insulation if necessary, to perfect the installation. Never delegate placement of insulation to be done without caring, in haste. The value of insulation placement is proportional to time spent.

Back to that now-disposed gage then. Don't believe it, even where it reads correctly in perhaps revealing fraud. Diligent work is harder to gage.