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A9.4 Calculation Procedures and Assumptions

Energy Standard for Buildings Except Low-Rise Residential Buildings 2016 of Illinois > Normative Appendix A Rated R-Value of Insulation and Assembly U-factor, C-Factor, and F-Factor Determinations > A9 Determination of Alternate Assembly U-Factors, C-Factors, F-Factors, or Heat Capacities > A9.4 Calculation Procedures and Assumptions

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The following procedures and assumptions shall be used for all calculations. R-values for air films, air spaces, insulation, and building materials shall be taken from Sections A9.4.1 through A9.4.4, respectively. In addition, the appropriate assumptions listed in Sections A2 through A8, including framing factors, shall be used.

A9.4.1 Air Films

Prescribed R-values for air films shall be as follows:

*R-Value*	Condition
0.17	All exterior surfaces
0.46	All semi-exterior surfaces
0.61	Interior horizontal surfaces, heat flow up
0.92	Interior horizontal surfaces, heat flow down
0.68	Interior vertical surfaces

A9.4.1.1

Exterior surfaces are areas exposed to the wind.

A9.4.1.2

Semiexterior surfaces are protected surfaces that face attics, crawlspaces, and parking garages with natural or mechanical ventilation.

A9.4.1.3

Interior surfaces are surfaces within enclosed spaces.

A9.4.2 Air Spaces

The R-value for air spaces shall be taken from Table A9.4.2-1 based on the effective emittance of the surfaces facing the air space from Table A9.4.2-2, provided the following criteria are satisfied:

The air space shall be an enclosed and unventilated cavity designed to minimize airflow into and out of the enclosed air space. Airflow shall be deemed minimized when the enclosed air space is located on the interior of the continuous air barrier and bounded on all sides by building components.
Reflective insulation as defined in ASTM Cl224, where used, shall be fitted closely around all non-heat-producing components and taped or otherwise sealed to eliminate gaps or voids through which air, dust, or water vapor has the potential to pass.
Nonparallel spaces shall use the average distance to determine the thickness of the air space.
Air spaces less than 0.5 in. thickness shall have no R-value.
The R-value for 3.5 in. air spaces shall be used for air spaces of that thickness or greater, provided that air space does not exceed 12 in. between the surfaces at any point.

Table A9.4.2-1 Values for Cavity Air Spaces^a

Component	*Air space* Thickness, in.**	Climate Zone 1 Effective Emittance				Climate Zone 2 Effective Emittance				Climate Zone 3 Effective Emittance
Component	*Air space* Thickness, in.**	0.05	0.20	0.50	0.82	0.05	0.20	0.50	0.82	0.05	0.20	0.50	0.82
Roof	0.50	2.5	1.9	1.2	0.9	2.4	1.8	1.2	0.9	2.2	1.7	1.1	0.9
	0.75	3.5	2.4	1.4	1.0	3.2	2.2	1.4	1.0	2.8	2.0	1.3	0.9
	1.50	5.6	3.1	1.7	1.1	4.9	2.9	1.6	1.1	4.2	2.5	1.5	1.0
	3.50	8.0	3.8	1.9	1.2	7.0	3.4	1.7	1.1	5.9	3.0	1.6	1.1
Wall	0.50	2.5	1.8	1.2	0.9	2.5	1.8	1.2	0.9	2.5	1.8	1.2	0.9
	0.75	2.8	2.0	1.3	0.9	2.8	2.0	1.3	0.9	2.8	2.0	1.3	0.9
	1.50	2.5	1.8	1.2	0.9	2.5	1.8	1.2	0.9	2.5	1.8	1.2	0.9
	3.50	2.6	1.9	1.3	0.9	2.6	1.9	1.3	0.9	2.6	1.9	1.3	0.9
Floor	0.50	1.6	1.3	1.0	0.8	1.8	1.4	1.0	0.8	1.9	1.5	1.1	0.8
	0.75	1.7	1.4	1.0	0.8	2.0	1.5	1.1	0.8	2.4	1.7	1.2	0.9
	1.50	1.9	1.5	1.1	0.8	2.5	1.8	1.2	0.9	3.2	2.1	1.3	0.9
	3.50	2.1	1.6	1.1	0.8	3.2	2.0	1.2	0.9	4.3	2.4	1.4	1.0
Component	*Air Space* Thickness, in.**	Climate Zone 4 Effective Emittance				Climate Zone 5 Effective Emittance				Climate Zone 6 Effective Emittance
Component	*Air Space* Thickness, in.**	0.05	0.20	0.50	0.82	0.05	0.20	0.50	0.82	0.05	0.20	0.50	0.82
Roof	0.50	2.0	1.6	1.1	0.8	1.9	1.5	1.1	0.8	1.8	1.4	1.0	0.8
	0.75	2.5	1.8	1.2	0.9	2.3	1.7	1.1	0.9	2.1	1.6	1.1	0.8
	1.50	3.5	2.2	1.3	0.9	3.1	2.0	1.3	0.9	2.8	1.9	1.2	0.9
	3.50	4.7	2.6	1.4	1.0	4.1	2.4	1.4	1.0	3.6	2.2	1.3	0.9
Wall	0.50	2.5	1.8	1.2	0.9	2.5	1.8	1.2	0.9	2.5	1.8	1.2	0.9
	0.75	2.8	2.0	1.3	0.9	2.8	2.0	1.3	0.9	2.8	2.0	1.3	0.9
	1.50	2.5	1.8	1.2	0.9	2.5	1.8	1.2	0.9	2.5	1.8	1.2	0.9
	3.50	2.6	1.9	1.3	0.9	2.6	1.9	1.3	0.9	2.6	1.9	1.3	0.9
Floor	0.50	2.1	1.6	1.1	0.8	2.2	1.7	1.1	0.9	2.3	1.7	1.2	0.9
	0.75	2.7	1.9	1.2	0.9	2.9	2.0	1.3	0.9	3.1	2.1	1.3	1.0
	1.50	3.9	2.4	1.4	1.0	4.3	2.6	1.5	1.0	4.7	2.7	1.5	1.1
	3.50	5.5	2.9	1.5	1.1	6.0	3.1	1.6	1.1	6.6	3.3	1.7	1.1
Component	*Air Space* Thickness, in.**	Climate Zone 7 Effective Emittance				Climate Zone 8 Effective Emittance
Component	*Air Space* Thickness, in.**	0.05	0.20	0.50	0.82	0.05	0.20	0.50	0.82
Roof	0.50	1.8	1.4	1.0	0.8	1.6	1.3	1.0	0.8
	0.75	2.0	1.6	1.1	0.8	1.8	1.4	1.0	0.8
	1.50	2.6	1.8	1.2	0.9	2.1	1.6	1.1	0.8
	3.50	3.2	2.0	1.3	0.9	2.4	1.7	1.2	0.9
Wall	0.50	2.5	1.8	1.2	0.9	2.5	1.8	1.2	0.9
	0.75	2.8	2.0	1.3	0.9	2.8	2.0	1.3	0.9
	1.50	2.5	1.8	1.2	0.9	2.5	1.8	1.2	0.9
	3.50	2.6	1.9	1.3	0.9	2.6	1.9	1.3	0.9
Floor	0.50	2.3	1.8	1.2	0.9	2.5	1.8	1.2	0.9
	0.75	3.2	2.2	1.4	1.0	3.4	2.3	1.4	1.0
	1.50	4.9	2.8	1.6	1.1	5.4	3.1	1.7	1.1
	3.50	6.9	3.4	1.7	1.1	7.7	3.7	1.8	1.2

a. Interpolation shall be permitted to be used for effective emittance values and air space thicknesses between those listed. Extrapolation below an effective emittance of 0.05 is not permitted.

Table A9.4.2-2 Emittance Values of Various Surfaces and Effective Emittances of Air Spaces

Surface	Average Emissivity e	Effective Emissivity of Air Space
		One Surface e; Other, 0.9	Both Surfaces Emissivity e
		Aluminum foil, bright	0.05	0.05	0.03^a
Metalized film, tested^b	0.05	0.05	0.03^a
Aluminum sheet	0.12	0.12	0.06
Aluminum coated paper, polished	0.20	0.20	0.11
Steel, galv., bright	0.25	0.24	0.15
Aluminum paint	0.50	0.47	0.35
Building materials: wood, paper, masonry, nonmetallic paints	0.90	0.82	0.82
Regular glass	0.84	0.77	0.72

a. When referencing Table A9.4.2-1. use an effective emittance of 0.05.

b. Tested emittance in accordance with ASTM C1224 at 0.05 or less.

For material emissivity properties not listed in Table A9.4.2-2, Equation A9.4-1 shall be permitted to calculate the effective emissivity for the air space.

(A9.4-1)

where

e_eff	=	effective emittance for the air space
e₁	=	surface 1 emittance
e₂	=	surface 2 emittance

A9.4.3 Insulation R-Values

Insulation R-values shall be determined as follows:

For insulation that is not compressed, the rated R-value of insulation shall be used.
For calculation purposes, the effective R-value for insulation that is uniformly compressed in confined cavities shall be taken from Table A9.4.3.
For calculation purposes, the effective R-value for insulation installed in cavities in attic roofs with steel joists shall be taken from Table A9.2-1.
For calculation purposes, the effective R-value for insulation installed in cavities in steel-framed walls shall be taken from Table A9.2-2.

Table A9.4.3 Effective R-Values for Fiberglass

*Insulation R-Value* at Standard Thickness**
Rated R-Value		38	30	22	21	19	15	13	11
Standard Thickness, in.		12	9.5	6.5	5.5	6	3.5	3.5	3.5
Nominal Lumber Size, in.	Actual Depth of Cavity, in.	*Effective Insulation R-Values* when Installed in a Confined Cavity**
2 × 12	11.25	37
2 × 10	9.25	32	30
2 × 8	7.25	27	26	22	21	19
2 × 6	5.5		21	20	21	18
2 × 4	3.5			14		13	15	13	11
	2.5							9.8
	1.5							6.3	6

A9.4.4 Building Material Thermal Properties

R-values for building materials shall be taken from Table A9.4.4-1. Concrete block R-values shall be calculated using the isothermal planes method or a two-dimensional calculation program, thermal conductivities from Table A9.4.4-2, and dimensions from ASTM C90. The parallel path calculation method is not acceptable.

Exception to A9.4.4

R-values for building materials or thermal conductivities determined from testing in accordance with Section A9.3.

Table A9.4.4-1 R-Values for Building Materials

Material	Actual Size, in.	*R-Value*
Carpet and rubber pad		1.23
Concrete at R-0.0625/in.	2	0.13
	4	0.25
	6	0.38
	8	0.5
	10	0.63
	12	0.75
Gypsum board	0.5	0.45
Gypsum board	0.625	0.56
Metal deck		0
Roofing, built-up	0.375	0.33
Soil at R-0.104/in.	12	1.25
Steel, mild	1	0.0031807
Stucco	0.75	0.08
Wood panels, 7/16 in.	0.438	0.62
Wood subfloor	0.75	0.94
Wood, 2 x 4 at R-1.25/in.	3.5	4.38
Wood, 2 x 6 at R-1.25/in.	5.5	6.88
Wood, 2 x 8 at R-1.25/in.	7.25	9.06
Wood, 2 x 10 at R-1.25/in.	9.25	11.56
Wood, 2 x 12 at R-1.25/in.	11.25	14.06
Wood, 2 x 14 at R-1.25/in.	13.25	16.56

Table A9.4.4-2 Thermal Conductivity of Concrete Block Material

Concrete Block Density, lb/ft³	Thermal Conductivity, Btu•in./h•ft²•°F
80	3.7
85	4.2
90	4.7
95	5.1
100	5.5
105	6.1
110	6.7
115	7.2
120	7.8
125	8.9
130	10.0
135	11.8
140	13.5

A9.4.5 Building Material Heat Capacities

The HC of assemblies shall be calculated using published values for the unit weight and specific heat of all building material components that make up the assembly.

A9.4.6 Metal Building U-factor Equations

For single-layer metal building roof and single-layer compressed metal building wall systems, the calculation procedure outlined in Section A9.4.6.1 shall be used to calculate the assembly U-factor. For double-layer metal building roof systems, the calculation procedure outlined in Section A9.4.6.2 shall be used to calculate the assembly U-factor. For single-layer in cavity and double-layer metal building wall systems, the calculation procedure outlined in Section A9.4.6.3 shall be used to calculate the assembly U-factor. Each of the above insulation methods and calculation procedures also shall be used where continuous insulation is applied to the assembly. The calculation procedures outlined in this section shall not be used for other metal building roof and wall systems.