Appendix A

Envelope Component Uo-Factor Calculations

 Appendix A

Envelope Component Uo-Factor Calculations

Appendix A documents the assumptions and equations used in calculating the envelope
component Uo-factors for the MECcheck™ compliance software, prescriptive packages, and trade-off
worksheet (DOE 1995c, 1995b, and 1995a) for the 1992, 1993, and 1995 editions of the Model Energy
Code (MEC) (CABO 1992, 1993, and 1995) and the 1998 and 2000 editions of the International Energy
Conservation Code (IECC) (ICC 1998 and 2000). Envelope components consist of ceilings, above-grade
walls, floors over unheated spaces, basement and crawl space walls, and slab-on-grade foundations.

The code(a) generally presents envelope component requirements in Uo-factors. The Uo-factor is a
measure of the rate of conductive heat transfer per unit area of any material(s). For simplicity, the
prescriptive package requirements are given in terms of R-values of insulating materials. The MECcheck
software allows the user to specify most components in terms of R-values. The trade-off worksheet
includes tables that allow the user to quickly ascertain an envelope component Uo-factor based on a
building description and the R-value of the insulating materials. Specifying inputs and requirements in
terms of R-value is advantageous because insulation R-values correspond to the products purchased by
builders and inspected by code officials.

Several details of the envelope component construction can impact envelope component Uo-
factors. To convert insulation R-values to overall component Uo-factors, assumptions must be made about
the typical construction of the envelope components. Note that construction materials and techniques
often vary from those assumed here and described below, but these differences will generally not have a
significant impact on the resulting Uo-factors.

The general equation for calculating heat flow through building envelope components is

U o = [U 1 × Area1 + U 2 × Area 2 + ...] / [Area1 + Area 2 + ...] (A.1)

where the subscripts identify different series of materials that present a different path of heat transfer; e.g.,
Area1 is the area between the framing and Area2 is the area of the framing. The U-factor is the inverse of
the sum of all the material R-values for each path of heat transfer and includes the insulating value of
surface air films. Equation (A.1) is sufficiently accurate unless any of the construction material is highly
conductive (e.g., steel framing).

As an example, for envelope components with wood frame construction, Equation (A.1) becomes

(a) The term, “the code,” refers to the 1992, 1993, and 1995 editions of the MEC and the 1998 and 2000
editions of the IECC in this Appendix.
A.1
 Uo =
Area STUDS / ∑R FRAMING PATH + Area INSULATION / ∑R INSULATION PATH
(A.2)
Area STUDS + Area INSULATION

A.1 Ceilings
Two common types of roof/ceiling construction are ceilings separated from roofs by an attic
space and ceilings without attics (flat, vaulted, or cathedral). Because of construction differences, the Uo-
factors for these two ceiling types are slightly different for equal insulation R-values. Prior to Version 3.2
of the MECcheck compliance materials, no differentiation was made between ceilings with and without
attics because the Uo-factor for the two types of roof/ceiling construction is sufficiently close. All ceiling
U-factors were calculated using the ceilings-with-attic construction as described in this section. A
comparison of Uo-factors for ceilings with and without attics is given in Section A.1.1.

MECcheck 3.2 and later versions include the distinction between ceilings with and ceilings
without an attic, primarily to improve clarity for the user as to which type of ceiling assembly they should
select. Some code officials reported confusion from users about how to enter ceilings without attics, and
some users were selecting the raised-truss option for ceilings without attics. Therefore, we modified the
software to include the following ceiling options:

• Flat Ceiling or Scissor Truss

• Cathedral Ceiling (no attic)
• Raised or Energy Truss
• Structural Insulated Panels (SIPs)
• Other

Additionally, the software displays an illustration of a raised-truss ceiling if the user selects that
option. The illustration helps clarify the definition of a raised-truss ceiling.

A.1.1 Flat Ceiling or Scissor Truss; Raised or Energy Truss

This section describes the algorithm used for flat ceilings and scissor trusses, as well as raised-
truss ceilings. In versions prior to MECcheck 3.2, this same algorithm was used for ceilings with and
without attics, entered in the software as an All Wood Joist/Rafter/Truss assembly. Refer to Section A.1.2
for the algorithm used for cathedral ceilings in MECcheck 3.2 and later versions.

The analysis assumed the use of blown fiberglass insulation, although batt insulation in ceilings is
also common. Insulation was assumed to cover the ceiling joists so that “voids” were negligible.
Equivalent batt and blown insulation R-values achieve similar Uo-factors, so the assumption of insulation
type has little effect. Ceiling joists or rafters were assumed to be at 24 in. on center (O.C.), occupying 7%
of the ceiling area for both ceiling types (ASHRAE 1989).

The American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc.

(ASHRAE) recommends an attic ventilation rate of 0.5 cfm/ft2 of ceiling area to control moisture
(ASHRAE 1989). A fully vented attic was assumed with a still-air film resistance above the insulation
and a 1-in. space between the insulation and the roof near the eaves for ventilation (the venting negates

A.2
the R-value of the roof materials). A prefabricated truss system was assumed because this system is most
common in new residential construction (Anderson and McKeever 1991). For truss members, 2x4
framing (DeCristoforo 1987) and a roof slope of 4/12 were assumed. Table A.1 shows the heat flow paths
for ceilings, and Equation (A.3) uses these results to compute the final Uo-factor of the ceiling
component.

A.3
 Table A.1. Heat Flow Paths for Ceilings

Description R-Value at Joists R-Value at Insulation

Percentage of Ceiling Area 7% 93%
Attic Air Film 0.61 0.61
Batt or Blown Insulation Rij Ric
Sheathing Rs Rs
Joists 4.38 --
1/2-in. Drywall 0.45 0.45
Inside Air Film 0.61 0.61
Total Path R-Value 6.05 + Rij + Rs 1.67 + Ric + Rs

0.07 0.93
Ceiling U o -Value = + (A.3)
6.05 + Rij + Rs 1.67 + Ric + Rs

where Rij = the effective overall R-value of the insulation above the ceiling joists as computed by
Equation (A.5).
Ric = the effective overall R-value of the ceiling cavity insulation between joists as computed
by Equation (A.4).
Rs = the rated R-value of the insulating sheathing (if any).

The effective insulation R-value may be less than the rated R-value because of limited space at
the eaves. Equations (A.4) and (A.5) account for the limited space for insulation at the eaves, which can
be alleviated by raising the trusses or using an oversized truss. For a standard truss, the space available at
the eaves was assumed to be 3.86 in. A standard truss was assumed in determining the prescriptive
packages. For a raised truss, the space available at the eaves was assumed to be 15.86 in. (3.86 in. + 12.0
in.). Equation (A.4) shows how the effective overall R-value of the ceiling cavity insulation (Ric) is
calculated. The effective insulation R-value is equal to the rated R-value if adequate space for the full
insulation thickness exists at the eaves.

Ric no min al
Ric = (A.4)
 yic full   yic full   yic full − yic eave 
1 +   ln   −  
 roof height   yic eave   roof height 

where Ricnominal = the rated R-value of the cavity insulation.

yicfull = the full thickness in inches of the cavity insulation
= Ricnominal / 2.5 (for blown fiberglass).
yiceave = the thickness in inches of the cavity insulation at the eaves. The space available at
the eaves is assumed to be 3.86 in. for a standard truss. If yicfull is greater than
3.86 in., yiceave is set to 3.86 in. For a raised truss, the space available is assumed to

A.4
 be 15.86 in. (3.86 in. + 12.0 in.). If yicfull is greater than 15.86 in., yiceave is set to
15.86 in.
roof height = the maximum height in inches at the center line of the house. A 56-in. height was
assumed, which corresponds to a 28-ft roof with a rise of 1 ft for each 3 ft across.

Equation (A.5) shows how the effective overall R-value of insulation is calculated for the
insulation above the ceiling joists (Rij). Equation (A.5) is the same as Equation (A.4), except 3.5 in. is
subtracted from the full insulation depth to account for the insulation displaced by the 2x4 joist. If the
truss is not raised, the height of the insulation at the eaves cannot be greater than 0.36 in. (3.86 in. - 3.5
in.). If the truss is raised, the height of the insulation above the eaves cannot be greater than 12.36 in.
(15.86 in. - 3.5 in.).

Ric no min al
Ric = (A.5)
 yijfull   yijfull   yijfull − yijeave 
1 +   ln   −  
 roof height   eave   roof height 
yij

where Rijnominal = the R-value of the insulation above the joist, which is the rated insulation R-value
(Ricnominal) minus the joist height (assumed to be 3.5 in.) x the resistance (assumed to
be 2.5°F·ft2h/Btu·in.).
= Ricnominal – (3.5 x 2.5)
yijfull = the full thickness of the insulation above the joist (in inches).
= (Ricnominal / 2.5) – 3.5.
yiceave = the thickness (in inches) of the insulation above the joists at the eaves. The space
available at the eaves is assumed to be 0.36 in. for a standard truss (3.86 in. – 3.5
in.). If yijfull is greater than 0.36 in., yijeave is set to 0.36 in. For a raised truss, the
space available is assumed to be 12.36 in. (15.86 in. – 3.5 in.). If yijfull is greater
than 12.36 in., yijeave is set to 12.36 in.
roof height = the maximum height in inches at the center line of the house. A 56-in. height was
assumed, which corresponds to a 28-ft roof with a rise of 1 ft for each 3 ft across.

Table A.2 shows some Uo-factors for ceilings calculated using this methodology. These Uo-
factors are used in the calculations to determine the prescriptive packages.

A.5
 Table A.2. Sample Uo-Factors for Ceilings

Average Insulation Insulation R-Value Uo-Factor of Ceiling

Nominal R-Value R-Value (Ric) Above Joists (Rij) Including Framing
11 11.0 2.2 0.082
19 18.5 9.2 0.051
30 27.3 15.9 0.035
38 32.5 19.1 0.030
38 + Raised Truss 38.0 29.2 0.025
49 38.0 22.2 0.026
49 + Raised Truss 48.6 39.9 0.020

A.1.2 Cathedral Ceiling (no attic)

For ceilings without attics in MECcheck 3.2 and later versions, the analysis assumed a fully
vented ceiling with a still-air film resistance above the insulation. Batt insulation was assumed because
vaulted ceilings typically have inadequate space for blown insulation. The rafters were modeled as 2x8 or
2x10 studs at 24 in. O.C. However, the effective thickness of the rafters was set equal to the thickness of
the insulation because heat flows directly out the side of the wood beyond the depth of the insulation.
Table A.3 shows the heat flow paths for ceilings without attics, and Equation (A.6) uses these results to
compute the final Uo-factor of the ceiling component.

Table A.3. Heat Flow Paths for Ceilings Without Attics

Description R-Value at Rafters R-Value at Insulation
Percentage of Ceiling Area 7% 93%
Ceiling Air Film 0.61 0.61
Batt Insulation -- Ri
Sheathing Rs Rs
Rafters Rr --
1/2-in. Drywall 0.45 0.45
Inside Air Film 0.61 0.61
Total Path R-Value 1.67 + Rr + Rs 1.67 + Ri + Rs

0.07 0.93
Ceiling U o -Value = + (A.6)
1.67 + Rr + Rs 1.67 + Ri + Rs

A.6
where Rr = the R-value of the wood rafters, which was assumed to be the thickness of the cavity
insulation multiplied by 1.25. The thickness of the batt cavity insulation was assumed to
be equal to the R-value of the cavity insulation (Ri) divided by 3.0.
= 1.25 x (Ri ÷ 3.0).
Ri = the rated R-value of the cavity insulation.
Rs = the rated R-value of the insulating sheathing if any.

A.1.3 Comparison of Uo-Factors for Ceilings With and Without Attics

As described above, all Uo-factors underlying the MECcheck materials prior to Version 3.2 were
based on buildings containing an attic space (i.e., a flat ceiling and a sloped roof). For typical
construction, the overall ceiling Uo-factors for buildings with and without attics are very close. The two
ceiling types were offered as separate options in MECcheck 3.2 and later versions primarily for
clarification rather than computational accuracy.

Table A.4 compares Uo-factors for ceilings with and without attics as calculated using the
methodologies described in Sections A.1.1 and A.1.2. This table shows that, for insulation R-values
commonly used in ceilings without attics, the difference in the Uo-factors between the two construction
types is small.

Table A.4. Comparison of Uo-Factors for Ceilings With and Without Attics

Batt Insulation Uo-Factor for Ceilings Uo-Factor for Ceilings Difference Between
R-Value With Attics Without Attics Construction Types
19 0.051 0.052 2%
30 0.035 0.034 3%

A.1.4 Structural Insulated Panels

At the time of this report, we were unable to find studies or reports on roof construction of
structural insulated panels (SIP). An approximate roof SIP adjustment is made by using the wall
correction factors. For a discussion of the algorithms used for wall, ceiling, and floor SIPs, refer to
Section A.2.5.

A.2 Walls
This section describes the calculation of wall Uo-factors, excluding windows and doors.

A.2.1 Wood-Frame Walls

Wall materials were assumed to be plywood siding, plywood and/or foam insulation sheathing on
the framing exterior, batt insulation, wood framing, and 1/2-in. gypboard on the interior. Walls with rigid
foam insulation were assumed to have plywood sheathing for 20% of the wall area to account for
structural support at corners. In the prescriptive packages, walls with insulation R-values equal to or less
than R-15 were modeled as having 2x4 studs at 16 in. O.C. and walls with insulation R-values greater
than R-15 were modeled as having 2x6 studs at 16 in. O.C.
A.7
 The 1992 MEC references the 1985 ASHRAE Handbook: Fundamentals (CABO 1992; ASHRAE
1985). The 1993 MEC references the 1989 ASHRAE Handbook: Fundamentals (CABO 1993; ASHRAE
1989). The percentage of wood-frame walls that constitute the framing area cited by these documents is
the same and was used for the wood-frame wall calculations in the 1992 and 1993 MECcheck materials.
Based on the assumptions in the ASHRAE handbooks, the 16 in. O.C. translates to a framing percentage
of 15% of the opaque wall area and the 24 in. O.C. translates to a framing percentage of 12% of the
opaque wall area. The 1995 MEC and later editions of the code reference the 1993 ASHRAE Handbook:
Fundamentals (CABO 1995; ASHRAE 1993). The 1993 ASHRAE handbook contains higher wood-
frame wall framing percentages─25% of the opaque wall area for 16-in. O.C. framing and 22% of the
opaque wall area for 24-in. O.C. framing. Wall construction heat flow paths are shown in Table A.5.
Equation (A.7) shows how opaque wall Uo-factors are calculated for the 1992 and 1993 MEC, and
Equation (A.8) shows how opaque wall Uo-factors are calculated for the 1995 MEC and the 1998 and
2000 IECC (ICC 1998 and 2000). Table A.6 shows wall Uo-factors for 16-in. O.C. walls and common
insulation R-values. These Uo-factors are used in the calculations to determine the prescriptive packages.

A.8
 Table A.5. Heat Flow Paths for Wood-Frame Walls

Description R-Value at Studs R-Value at Insulation

Outside Air Film 0.25 0.25
Plywood Siding 0.59 0.59
Sheathing Rs Rs
Wood Studs Rw --
(a)
Insulation -- Ri
1/2-in. Gypboard 0.45 0.45
Inside Air Film 0.68 0.68
Total Path R-Value 1.97 + Rs + Rw 1.97 + Rs + Ri
(a) If the nominal R-value is less than R-11, R-0.9 is added to account for the air space.

For the 1992 and 1993 MEC:

 0.15 or 0.12 0.85 or 0.88 

1.97 + Rs + Rw + 1.97 + Rs + Ri  0.80 +
Wall U o -Factor =   (A.7)
 0.25 or 0.12 0.85 or 0.88 
1.97 + 0.83 + Rw + 1.97 + 0.83 + Ri  0.20
 

For the 1995 MEC, and 1998 and 2000 IECC:

 0.25 or 0.22 0.75 or 0.78 

1.97 + Rs + Rw + 1.97 + Rs + Ri  0.80 +
Wall U o -Factor =   (A.8)
 0.25 or 0.22 0.75 or 0.78 
1.97 + 0.83 + Rw + 1.97 + 0.83 + Ri  0.20
 

where Rs = the R-value of the insulating sheathing (entered in the software as continuous insulation).
If no insulating sheathing is indicated, the sheathing is assumed to be plywood with an
R-value of 0.83. If insulating sheathing is used, only 80% of the net wall is assumed to
be covered by the insulating sheathing. The other 20% is assumed to be covered with
plywood (R-value = 0.83).
Rw = the R-value of the wood framing members. The R-value of the wood framing members
was assumed to be R-4.38 for 2x4 construction and R-6.88 for 2x6 construction.
Ri = the rated R-value of the cavity insulation.

A.9
 Table A.6. Sample Uo-Factors for 16-in. O.C. Wood-Frame Walls

1992 and 1993 1995 MEC, 1998

Batt Insulation Sheathing MEC Wall and 2000 IECC
R-Value Insulation R-Value Framing R-Value Uo-Factor(a) Wall Uo-Factor(a)
11 0.83 4.38 0.083 0.089
13 0.83 4.38 0.075 0.082
19 0.83 6.88 0.055 0.060
21 0.83 6.88 0.051 0.057
19 4 6.88 0.047 0.055
19 5 6.88 0.046 0.054
19 7 6.88 0.043 0.052
(a) Wall Uo-factors calculated for compliance with the 1995 MEC and 1998 and 2000 IECC are higher than those
for the 1992 and 1993 MEC because of the higher assumed wood framing area.

A.2.2 Steel-Frame Walls

Equation (A.1), which calculates heat loss rates through parallel paths of heat transfer (i.e.,
framing and insulation), is not accurate for steel-frame walls because of the high conductivity of the steel
studs. Combined stud/insulation R-values (Re), which more accurately account for the metal stud
conductivity, were calculated from Table 502.2.1b of the 1995 MEC (CABO 1995). Table A.7 shows
these combined stud/insulation R-values, which are referred to as equivalent R-values. Given these
equivalent R-values, the steel-frame wall Uo-factors are the inverse of the sum of the wall layer R-values
as shown in Table A.8 and Equation (A.9).

Table A.7. Equivalent R-Values for Steel-Frame Walls

Equivalent R-Value Equivalent R-Value

Nominal R-Value of (16-in. framing (24-in. framing
Insulation spacing) spacing)
0.0 - 10.9 0.0 0.0
11.0 - 12.9 5.5 6.6
13.0 - 14.9 6.0 7.2
15.0 - 18.9 6.4 7.8
19.0 - 20.9 7.1 8.6
21.0 - 24.9 7.4 9.0
25.0+ 7.8 9.6

A.10
 Table A.8. Heat Flow Paths for Steel-Frame Walls

Description R-Value
Outside Air Film 0.25
Plywood Siding 0.59
Sheathing Rs
(a)
Equivalent R-Value Re
1/2-in. Gypboard 0.45
Inside Air Film 0.68
Total Path R-Value 1.97 + Rs + Re
(a) If the nominal R-value is less than R-11, R-0.9 is added to account
for the air space.

1.0
Steel-Frame Wall U o -Value = (A.9)
1.97 + Rs + Re

where Rs = the R-value of the insulating sheathing. If no insulating sheathing is indicated, the
sheathing is assumed to be plywood with an R-value of 0.83. The entire wall was
assumed to be covered with insulation sheathing.
Re = the equivalent R-value, determined by the rated cavity insulation R-value and the spacing
of the framing members. Table A.7 lists the equivalent R-values used.

A.2.3 Mass Walls

MECcheck 3.0 uses the same three mass wall types for above-grade mass walls, basement walls,
and crawl space walls. Table A.9 lists these wall types and gives the R-value assigned to that uninsulated
wall type in MECcheck. The following sections describe how these assembly types were chosen, how
their uninsulated wall R-values were assigned, and how the Uo-factors for the entire mass wall assemblies
are calculated for the proposed building in the MECcheck software. This section does not address how
the MEC requirements for high-mass walls are calculated. Section 6.3.3 of this document explains how
the software incorporates the credit the MEC gives to high-mass walls.

Table A.9. MECcheck Mass Wall Types and R-Values

Mass Wall Type Uninsulated Wall R-Value

Solid Concrete or Masonry R-1.6
Masonry Block with Empty Cells R-1.8
Masonry Block with Integral Insulation R-2.4

MECcheck also includes an option for log walls, which are also considered mass walls (see Section
A.2.4).

A.11
 Selection of Mass Wall Types

In looking at the small differences between the three mass wall R-values given in Table A.9, it is
arguable whether the three mass wall options are necessary. They could be combined into a single
category as was done in previous versions of MECcheck. However, input received from Wisconsin state
officials indicated a concern with users incorrectly entering the R-value of masonry core inserts under the
Cavity R-Value field. Offering the Masonry Block with Integral Insulation option helps alleviate this
confusion in the software and gives some credit to builders using the insulated block. When Masonry
Block with Integral Insulation is selected, the software further issues a warning message that informs
users NOT to enter the R-value of the inserts because they are already accounted for. Using these three
options more closely aligns MECcheck with the COMcheck-EZ options because these same mass wall
types and their definitions match those used for COMcheck-EZ. However, COMcheck-EZ distinguishes
between wall thickness, with walls <8” and walls >8” being separate assemblies.

Wisconsin officials further expressed concern that their builders using filled blocks were not
receiving enough credit. Wisconsin builders are apparently using blocks with R-values of up to R-5.
While our conclusions did not justify generically assigning an R-5 to filled block products, MECcheck
does support an “Other” wall category that can be used to enter these and other specialty mass wall
products that substantially exceed the default R-values assigned.

As discussed in the following sections, differences in concrete wall characteristics (such as

thickness, density, and web characteristics) generally have less than an R-1 impact, but clearly some of
the systems described in the section entitled, “Other Wall R-Values,” have a more significant impact.
Direct support for these specialty products is not provided in MECcheck. More detailed coverage of these
options would allow users to more accurately model mass wall types. Not including these options could
make it more difficult for builders to use the specialty products and does not help support the more
energy-efficient products mentioned. However, adding these options would complicate the software for
other users. Concrete above-grade exterior walls only comprise about 4.4% of residential construction,
with most of this construction in the south (1995-Residential Energy Consumption Survey). Specialty
systems would comprise an even smaller percentage. Making MECcheck more complex in an attempt to
address the needs of this small percentage and all of the other variations on mass walls is not advised.
Again, the “Other” wall option can be used.

Another difficulty in directly supporting specialty products is determining the R-value to assign
to those products. In some cases, manufacturer-reported values for some specialty products may be
inflated. As an example, ICON block inserts were reported by the manufacturer to have a system R-value
of 5.8, but tests revealed a measured R-value of only 3.5 (Energy Design Update 1993). High-mass
products may report an “effective” R-value that gives a substantial credit for thermal mass, while the
credit for thermal mass is provided elsewhere in the code (and in MECcheck) and should not be included
in the R-value.

Solid Concrete or Masonry Wall R-Value

Solid Concrete or Masonry wall types are defined as solid precast or poured-in-place concrete as
well as concrete masonry units (CMUs) with grouted cells having grout in 50% or more of the CMU

A.12
cells. The R-value of grouted masonry more closely resembles solid concrete than masonry with empty
cells.

According to Martha Van Geem of Construction Technology Laboratories, Inc., 144 lb/ft2
concrete is by far the most common in residential construction.(a) For basements, the nominal thickness of
plain concrete walls should be 8 in. or more for walls 7 ft. or more below grade(b). Tables A.10 and A.11
show R-values for solid concrete of various densities and thicknesses from ASHRAE Standard 90.1R,
Appendix A (ASHRAE 1996) and U-factors for stone and gravel or stone aggregate concretes from the
1997 ASHRAE Handbook: Fundamentals (ASHRAE 1997, page 24.7), respectively.

Table A.10. R-Values (U-Factors) from Standard 90.1R

Solid Concrete
3
Density (lb/ft ) 6-in. Thickness 8-in. Thickness
85 R-2.3 (0.44) R-2.7 (0.37)
115 R-1.5 (0.65) R-1.8 (0.57)
144 R-1.2 (0.81) R-1.4 (0.74)

Table A.11. U-Factors from ASHRAE 1997 Fundamentals Handbook

Stone and Gravel or Stone Aggregate Concretes

Median R-Value R-Value with Air
Density (lb/ft3) R-Value per in. for 8 in. Films (0.25+0.68)
130 0.08-0.14 0.88 1.81
140 0.06-0.11 0.68 1.61
150 0.05-0.10 0.60 1.53

The variation of R-value over common ranges of density and thickness is less than R-1. This
small variance does not merit breaking down the wall assembly categories further by density or thickness.

Using the ASHRAE 1997 handbook as the primary reference, Solid Concrete and Masonry
assembly types for both above-grade and below-grade walls assume an 8-in. wall and are assigned an R-
value of R-1.6 for the uninsulated wall. This value includes air films of R-0.25 + R-0.68.

(a) Assumptions and equivalent R-values for solid concrete constructions based on a personal
communication with Martha Van Geem, Construction Technology Laboratories, Inc. Calculation of
concrete wall based on energy calculations and data.

(b) See Building Foundation Design Handbook, Table 7-11, page 184 (Carmody 1998).

A.13
 Masonry Block with Empty Cell Wall R-Value and Masonry Block with Integral Insulation
Wall R-Value

Masonry Block with Empty Cells is defined as CMUs with at least 50% of the CMU cells free of
grout.

Masonry Block with Integral Insulation is defined as CMUs with integral insulation such as
perlite or rigid foam inserts.

Bruce Wilcox indicated that 8-in. medium-weight, partially-grouted CMU was commonly used
for residential construction.(a) Kosny and Christian (1995) report that “normal-weight” (120-to-144 lb/ft2)
blocks are by far the most common. Steve Szoke indicated the high end of medium-weight blocks are
common, and suggested using ungrouted as a default.(b) Tables A.12 and A. 13 show the R-values and U-
factors from ASHRAE Standard 90.1R (ASHRAE 1996) and U-factors from the 1997 ASHRAE
Handbook: Fundamentals (ASHRAE 1997).

Table A.12. R-Values and U-Factors (including air films) from Standard 90.1R
Partial
Density (lb/ft3) Grouted, Partial Grouted, Unreinforced, Unreinforced,
and Thickness Solid Grouted Cells Empty Cells Insulated Cells Empty Cells Insulated
85
6 in. R-1.8 (0.57) R-2.2 (0.46) R-2.9 (0.34) R-2.5 (0.40) R-5.0 (0.20)
8 in. R-2.0 (0.49) R-2.4 (0.41) R-3.6 (0.28) R-2.7 (0.37) R-6.6 (0.15)
115
6 in. R-1.5 (0.66) R-1.9 (0.54) R-2.4 (0.41) R-2.2 (0.46) R-3.8 (0.26)
8 in. R-1.7 (0.58) R-2.1 (0.48) R-2.8 (0.35) R-2.3 (0.43) R-4.8 (0.21)
135
6 in. R-1.4 (0.73) R-1.7 (0.60) R-2.0 (0.49) R-1.9 (0.53) R-2.9 (0.35)
8 in. R-1.5 (0.65) R-1.8 (0.55) R-2.4 (0.42) R-2.0 (0.49) R-3.6 (0.28)

Table A.13. U-Factors from ASHRAE 1997 Fundamentals Handbook

Normal Weight Aggregate (sand and gravel), 8 in.
R-Value with Air Films
Type R-Value of Block Only (0.25+0.68)
Empty 0.97-1.11 1.90-2.04
Perlite Fill 2.0 2.93

(a) Assumptions and equivalent R-values for block masonry constructions were based on a personal
communication with Bruce Wilcox, Berkeley Solar Group.

(b) Assumptions and equivalent R-values for block masonry constructions were based on a personal
communication with Stephen Szoke, Portland Cement Association.
A.14
 Vermiculite Fill 1.37-1.92 2.30-2.85

Kosny and Christian (1995) report 2-core 12-in. blocks have an R-value of slightly less than R-2
(apparently this R-value does not include air films).

Over common densities, the density and thickness does not make much difference─less than R-1.
Insulated cells do not have a significant impact, particularly when grouting is used, suggesting that it is
not important to allow the user to specify these inputs. However, MECcheck 3.0 does include an option
for Masonry Block with Integral Insulation for reasons sited in the previous section entitled, “Selection of
Mass Wall Types.”

We used the Standard 90.1R table to establish default values because the table covers the variety
of concrete blocks. The software currently assumes an 8–in. 135-lb/ft3 block with partial grouting based
on a recommendation by Bruce Wilcox and because assuming partial grouting is more conservative than
assuming no grouting. The software option for Masonry Block with Empty Cells allows for up to 50%
grouting. R-1.8 is used for this option, based on Partial Grouted, Cells Empty in the Standard 90.1R
table. R-2.4 is used for Masonry Block with Integral Insulation, based on Partial Grouted, Cells
Insulated in the Standard 90.1R table. These values include air films of R-.25 + R-.68.

Other Wall R-Values

Several mass walls types could be classified as specialty products. The following results from
Kosny and Christian (1995) describe specialty mass wall products, some of the features of these products,
and their impact on R-value.

Improved Block Design with Insulation Fill: A “cut web” design with 12-in. normal-density
block has an R-value of R-5.4, more than double the R-value of a 2-core 12-in. block. A similar
multicore block is rated at R-3.5 if the core is left uninsulated and R-6.8 if the core is insulated. Self-
locking blocks with continuous insulation in the middle (like a sandwich) have tested R-values of about
R-8 to R-10. Product literature for one such product (Thermalock) reports R-14 for 8-in. blocks, R-18 for
10-in. blocks, and R-24 for 12-in. blocks. Supposedly, these products are to be installed with no thermal
bridge by mortar, but we do not know if this type of installation is typical.

Density: Density is more-or-less bimodal. The most commonly used heavy concrete has
densities ranging from about 120 to 140 lb/ft3. Other products, such as autoclaved aerated concrete
(AAC, e.g., hebel block), lightweight expanded clay aggregate, and expanded polystyrene bead concrete,
have much lower densities. Table A.14 shows the density and R-value of specialty products.

Table A.14. Density and R-Value of Specialty Products

Density R-Value per in.
Expanded Shale, Clay, and Slate Concrete 80-100 0.27 to 0.40
Lightweight Expanded Clay Aggregate 28-40 0.90 to 1.07
Concrete
Wood Concrete 28-40 0.41 to 0.90

A.15
 Autoclaved Aerated Concrete 30-40 0.95
Expanded Polystyrene Bead Concrete 25-70 0.89 (30 lb/ft3)

Mortar Joints: Kosny and Christian (1995) report that mortar has little effect on hollow,
normal-weight, 2-core, 12-in. blocks–the R-value is reduced by less than 1%. If the cores are insulated,
the mortar can result in a 2% to 5% reduction in R-value. Kosny and Christian report the mortar joint
covers 4% to 10% of the total wall vertical area and assume an R-value of 0.2 per in. The use of mortar
in any concrete walls with high R-values (insulation inserts, low-density concretes) can cause a major
decrease to the R-value if it establishes a bridge across the insulation.

Mass Wall Uo-Factors

Uo-factors for mass walls are determined by adding an R-value for the uninsulated wall and the
insulation system (which accounts for air films and other materials). For exterior insulation, the
insulation was assumed to cover the entire wall. Equation (A.10) computes the U-factor of a mass wall
with interior and/or exterior insulation. For interior insulation, an interior furring system was assumed.
Table A.15 lists equivalent R-values for interior furring and insulation systems.

1
Mass Wall U o = (A.10)
Reff + Rwall + Rcont

where Reff = the effective R-value of an interior furring and insulation system as determined by the
rated R-value of the cavity insulation.
Rwall = the R-value of the uninsulated wall (as determined in the previous sections).
Rcont = the rated R-value of the exterior continuous insulation.

A.16
 Table A.15. Effective R-Values for Interior Furring Systems(a)
Thickness of Framing
Nominal R-Value (in.) Effective R-Value
0 0.75 1.4
1 0.75 1.4
2 0.75 2.1
3 0.75 2.7
4 1.0 3.4
5 1.5 4.4
6 1.5 4.9
7 2.0 5.9
8 2.0 6.4
9 2.5 7.4
10 2.5 7.9
11 3.5 9.3
12 3.5 9.8
13 3.5 10.4
14 3.5 10.9
15 3.5 11.3
16 5.5 13.6
17 5.5 14.2
18 5.5 14.7
19 5.5 15.3
20 5.5 15.8
21 5.5 16.3
(a) The framing thickness varies with R-value. All values include 0.5-in.
gypsum wallboard on the inner surface (interior surface resistances not
included). The framing was assumed to be 24-in. on-center, and the
insulation was assumed to fill the furring space. The framing was
assumed to have an R-value of 1.25/in.

A.2.4 Log Walls

Log wall Uo-factors are based on log thickness plus any additional insulation entered by the user.
Table A.16 correlates log wall thicknesses and nominal Uo-factors. Equation (A.11) is used to determine
the Uo-value of the log walls plus additional insulation entered by the user (assumed to cover the entire
wall).

1.0
Log Wall U-Factor = (A.11)
Log R-Value + Insulation R-Value

where Log R-value = the midpoint of the nominal R-value range given in Table A.16.

A.17
 Table A.16. Log Wall R-Values and Uo-Factors(a)
Nominal Log Average Weight Heat Capacity Nominal Nominal
Thickness (in.) lb/ft2(b) Btu/ft2(c) R-Value(d) Uo-Factor
5 14 6 6.4-7.4 0.149
6 14 6 7.5-8.3 0.125
7 24 9 8.6-1.0.0 0.108
8 24 9 9.7-11.3 0.095
9 24 9 10.8-12.6 0.086
10 32 12 11.0-13.9 0.080
12 32 12 14.1-16.5 0.065
14 32 12 16.3-19.1 0.057
16 42 16 18.4-20.8 0.051
(a) Reproduced from a personal communication from T.J. Cadenas, Steven Winter Associates, Inc.
(b) Average weight computed on the basis of a wood density range at 12% moisture content of 21.7
lb/ft3 for west coast woods and cedar to 41.2 lb/ft3 for southern pine (ASHRAE 1985).
(c) Computed on the basis of wood specific heat at 12% moisture content of 0.39 Btu/lb°F at 75°F
(ASHRAE 1985).
(d) R-values assume a resistance per inch range of 1.1-1.3 plus 0.85 for film resistance. A wood
density range of 21.7 lb/ft3 at 12% moisture content for west coast woods and cedar to 41.2 lb/ft3 for
southern pine. A specific heat of 0.39 Btu/lb·°F at 12% moisture content (ASHRAE 1985).

Note that the MEC and IECC contain a mass wall credit for walls having a heat capacity greater
than or equal to 6 Btu/ft2⋅°F. The code states that, “Solid wood walls having a mass greater than or equal
to 20 lb/ft2 have heat capacities equal to or exceeding 6 Btu/ft2⋅°F.” According to the data in Table A.16,
5-in. and 6-in. log walls are borderline in meeting these criteria, with the heat capacity given just at the
lower boundary but the weight falling below 20 lb/ft2. Because it was unclear whether 5-in. and 6-in. log
walls met the mass wall criteria, we originally excluded them as an option in MECcheck. However, input
from Vermont users suggested that this log size is commonly used in log home construction in Vermont
and that it should be included in MECcheck. MECcheck 3.0 now allows the user to select 5-in. and 6-in.
log walls, but the mass wall credit is not applied to them.

A.2.5 Structural Insulated Panels

Wall Panels

SIPs typically have ½-in. fiberboard sheathings and an EPS foam core. Panels have an edge
stiffener, which also is used as the nailing strip for connections. Corners and window/door openings all
require the foam core be replaced with wood framing members. MECcheck instructs users to provide the
manufacturer-reported R-value of the SIP panel in the continuous R-value field. Manufacturer-reported
R-values are typically clear-wall R-values–they do not include connections and framing effects.

A.18
 For SIP panels, Oak Ridge National Laboratory (ORNL) has reported the difference between the
clear-wall R-value and overall wall R-value as 12.5% (ASHRAE Transactions V. 104, Table 5). The
ORNL Whole-Wall Thermal Performance Calculator estimates the whole-wall R-value to be 88.3% of the
clear-wall R-value in a typical single-family dwelling (an 11.7% difference) (ORNL 2001).

From these results, we adopted an adjustment factor of 12.5% for use in MECcheck for
calculating the overall R-value of SIP exterior walls, which is the more conservative of the two results.
Because the manufacturer-reported R-values do not include air films, we assumed the heat flow paths
shown in Table A.17.

Table A.17. Assumed Heat Flow Paths for Wall Panels

Description R-Value
Outside Air Film 0.25
Wall Panels Rm * 0.875
1/2-in. Gypboard 0.45
Inside Air Film 0.68
Total Path R-Value 1.38 + (Rm * 0.875)
Rm = the manufacturer’s reported R-value.

Floors Panels

No studies or reports are available for floor construction of SIP panels. An approximate floor
adjustment is made using wall correction factors listed in the Whole-Wall Thermal Performance
Calculator for stress-skin walls. The only heat flows listed in this table considered applicable to the floor
are the clear-wall (42.42 Btu/h·ºF) and wall/floor (1.86 Btu/h·ºF) heat flows. Adding these heat flows
gives 44.28 Btu/h·ºF, which is approximately 96% of the clear-wall heat flow. Therefore, an adjustment
of 4% is warranted.

The floor joists consist of ½-in. fiberboard web. Based on the percentage of joist web area of a
typical 4-x 8-ft panel, the fiberboard web comprises about 1% of the floor area. The adjustment factor is
increased by 1% to account for the heat flow through the webs, which are not a factor in wall
construction.

Assuming that the MECcheck user provides a clear-wall R-value of the stress-skin floor panel, a
total adjustment factor of 5% was adopted for use in calculating the overall R-value of SIP floors (a 4%
adjustment plus 1% for the webs). Because the manufacturer-reported R-values do not include air films,
we assumed the heat flow paths shown in Table A.18.

A.19
 Table A.18. Assumed Heat Flow Paths for Floor Panels

Description R-Value
Unheated Space Air Film 0.92
Floor Panels Rm * 0.95
Carpet and Pad 1.23
Inside Air Film 0.92
Total Path R-Value 3.07 + (Rm * 0.95)
Rm = the manufacturer’s reported R-value.

Roof Panels

No studies or reports are available for roof construction of SIP panels. An approximate roof
adjustment is made using wall correction factors listed in the Whole-Wall Thermal Performance
Calculator for stress-skin walls. A conservative approach assumes that the window, door, and corner
framing of the walls are analogous to the roof ridge framing in the ceilings. If the heat flow through the
wall/floor framing is removed from consideration, the total heat flow from this table would be 46.21
Bth/h·ºF (48.07 - 1.86). This heat flow is approximately 92% of the clear-wall heat flow, so an
adjustment of 8% is warranted. An additional 1% was added for the wood portion of the joist members,
as was done for floors.

Assuming that the MECcheck user provides a clear-wall R-value of the stress-skin ceiling panel, a
total adjustment factor of 9% was adopted for use in calculating the overall R-value of SIP ceilings (an
8% adjustment plus 1% for the webs). Because the manufacturer-reported R-values do not include air
films, we assumed the heat flow paths shown in Table A.19.

Table A.19. Assumed Heat Flow Paths for Roof Panels

Description R-Value
Ceiling Air Film 0.61
Roof Panels Rm * 0.91
1/2-in. Drywall 0.45
Inside Air Film 0.61
Total Path R-Value 1.67 + (Rm * 0.91)
Rm = the manufacturer’s reported R-value.

A.2.6 Insulated Concrete Forms

Insulated concrete Forms (ICFs) consist of two rigid-board insulation sheathings that serve as a
permanent form for poured-in-place concrete walls. The insulation sheathings are connected by plastic or
metal links that keep the sheathings in position and also serve as stirrups or reinforcements for the
concrete wall. MECcheck instructs users to provide the manufacturer-reported R-value of ICFs in the
A.20
continuous R-value field. Manufacturer-reported R-values are typically clear-wall R-values–they do not
include connections and framing effects.

The ORNL tests (ASHRAE Transactions V. 104, Table 5), show that the difference between the
clear-wall R-value and the overall wall R-value is 9.5%. These ORNL calculations take into account the
additional framing in corners, window/door frames, and wall/roof and wall/floor interfaces. A typical
ICF wall analyzed using the ORNL Whole-Wall Thermal Performance Calculator shows that the whole-
wall R-value is 89% of the clear-wall R-value (an 11% difference) (ORNL 2001).

Assuming that the MECcheck user provides a clear-wall R-value of an ICF construction, an
adjustment factor of 11% was adopted for use in determining the overall effective R-value, which is the
more conservative of the two results. Tables A.20 and A.21 lists the R-values used to calculate the overall
effective R-Value for above- and below-grade ICF walls.

Table A.20. Above-Grade ICF Walls

Description R-Value
Outside Air Film 0.25
ICF Clear Wall Rm * 0.89
1/2-in. Gypboard 0.45
Inside Air Film 0.68
Total Path R-Value 1.38 + (Rm * 0.89)
Rm = the manufacturer’s reported R-value.

Table A.21. Below-Grade ICF Walls

Description R-Value
ICF Clear Wall Rm * 0.89
Inside Air Film 0.68
Total Path R-Value 0.68 + (Rm * 0.89) +
Soil Impact
Rm = the manufacturer’s reported R-value.

A.3 Floors Over Unheated Spaces

A.3.1 All-Wood Joist/Truss

We assumed that floors over unheated spaces are constructed of batt insulation, wood framing, a
¾-in. wood subfloor, and carpet with a rubber pad. The floor joists were modeled as 2x10 studs at 16-in.
O.C. (DeCristoforo 1987) occupying 10% of the floor area. The effective depth of the joists for the
thermal calculation was set equal to the depth of the insulation. This thickness was used because heat
flows directly out of the sides of the joists beyond the depth of the insulation. Table A.22 shows the heat
flow paths for floors over unheated spaces, and Equation (A.12) uses these results to compute the final
A.21
floor component Uo-value. Table A.23 shows some Uo-factors for floors over unheated spaces as
calculated by this methodology. These Uo-factors are used in the calculations to determine the
prescriptive packages.

Table A.22. Heat Flow Paths for Floors Over Unheated Spaces

Description R-Value at Joists R-Value at Insulation

Percentage of Floor Area 10% 90%
Unheated Space Air Film 0.92 0.92
Insulation -- Ri
Joists Rj --
Carpet and Pad 1.23 1.23
¾-in. Wood Subfloor 0.94 0.94
Inside Air Film 0.92 0.92
Total Path R-Value 4.01 + Rj 4.01 + Ri

0.1 0 .9
Floor U o -Value = + (A.12)
4.01 + Rj 4.01 + Ri

where Rj = the R-value of the wood joists, which was assumed to be the thickness of the cavity
insulation multiplied by 1.25. The thickness of the batt cavity insulation was assumed to
be equal to the R-value of the cavity insulation (Ri) divided by 3.0.
= 1.25 x (Ri ÷ 3.0).
Ri = the rated R-value of the cavity insulation.

Table A.23. Sample Uo-Factors for Floors Over Unheated Spaces

Batt R-Value Uo-Value of Floor Including Framing
0 0.250
11 0.072
13 0.064
19 0.047
30 0.033

A.3.2 Structural Insulated Panels

No studies or reports were found for floor construction of SIPs. An approximate floor SIP
adjustment is made by using the wall correction factors. For a discussion of the algorithms used for wall,
ceiling, and floor SIPs, refer to Section A.2.5.

A.22
A.4 Basement Walls
The methodology for calculating heat loss through basement walls was adapted from the 1993
ASHRAE Handbook: Fundamentals (ASHRAE 1993, p. 25.10-25.11). Both the proposed and required
UA calculations take into account the effect of the soil surrounding below-grade walls.

The soil R-value is computed for each 1-ft increment of wall below grade, based on the user’s
Wall Height and Depth Below Grade inputs. Table A.24 gives the heat loss factors for an uninsulated
wall as given in the 1993 ASHRAE handbook (ASHRAE 1993). The combined R-value of the
uninsulated wall and air-films in the ASHRAE values was determined to be approximately R-1.6.
Column D of Table A.24 gives the R-value attributed to the soil at each 1-ft. increment after the wall R-
value of R-1.6 has been deducted.

A.4.1 Proposed UA Calculation

To compute the proposed UA, the foundation dimensions and insulation characteristics are
obtained from the user.

• height of wall
• depth below grade
• depth of insulation
• R-value of insulation
• wall area.

The “depth of insulation” refers to the distance the insulation extends vertically from the top of
the foundation wall downward. No additional credit is given for insulation depths greater than the height
of the wall.

The basement perimeter is also used in the UA calculation and is estimated from Equation A.13.

Wall Area
Perimeter = (A.13)
Wall Height

The proposed wall UA is calculated as:

i =1
 1 
proposed UA = ∑  wall R -value[i] + soil R -value[i]  * area[i]
n
(A.14)

where wall R-value[i] = the R-value of the wall assembly for increment i, based on the wall type and
the insulation configuration.
soil R-value[i] = the R-value of the soil for increment i, based on the depth below grade of
increment i (see Table A.24).
area[i] = the perimeter times the height, which is 1 for a complete increment, but may be
a fraction of 1, depending on the configuration.
n = the wall height, rounded up to the nearest whole number.
A.23
 Equation A.14 is calculated separately for the above-grade UA (in which case the soil R-value is
0) and the below-grade UA. The total building UA is the sum of these separate calculations. For partial
increments, the area is adjusted to reflect only the area under consideration. For example, if the user
defines a wall 1.5 ft above-grade, then the above-grade portion is computed based on two increments,
with the second increment having only one-half the area of the first increment (perimeter * 0.5).
Likewise, partial increments are computed if the user’s depth of insulation does not fall in whole-number
increments, in which case the wall R-value may vary over the increment. Table A.24 gives the soil R-
values used in Equation A.14, based on the depth of the increment under consideration.

Table A.24. Soil R-Values

A B C D
Depth Below Heat Loss (Btu/ft2 h ºF) R-Value of Uninsulated R-Value of Soil Only
Grade (ft) for Uninsulated Wall Wall and Soil (1 / B) (C – 1.6)
0-1 0.410 2.439 0.839
1-2 0.222 4.505 2.905
2-3 0.155 6.452 4.852
3-4 0.119 8.403 6.803
4-5 0.096 10.417 8.817
5-6 0.079 12.658 11.058
6-7 0.069 14.493 12.893
7-8 0.061 16.393 14.793
8-9 0.055 18.182 16.582
(a)
9-10 0.049 20.408 18.808
(a) Depths below 10 ft assume the 9-to-10-ft soil R-value.

A.4.2 Required UA Calculation

The MEC does not consider the surrounding soil in determining the basement wall Uo-factor
requirements (Table 502.2.1, Footnote 5 in the 1992 and 1993 MEC [CABO 1992, 1993]; Table 502.2.1a,
Footnote 5 in the 1995 MEC [CABO 1995]; Table 502.2, Footnote ‘e’ in the 1998 and 2000 IECC [ICC
1998, 2000). To directly compare the required Uo-factor specified by the code (which does not include
soil) to the proposed building Uo-factor (which does include soil), the code requirement is adjusted to
include the impact of the soil.

The required wall UA is calculated as:

 
i =1  
 1  * area[i]
required UA = ∑  1 
(A.15)
n
 + soil R -value[i] 
 MEC U o 

A.24
where MECUo = the MEC/IECC basement wall Uo requirement for the given location.
soil R-value[i] = the R-value of the soil for increment i, based on the depth below grade of
increment i (see Table A.24).
area[i] = the perimeter times the height, which is 1 for a complete increment, but may
be a fraction of 1, depending on the configuration.
n = the wall height, rounded up to the nearest whole number.

A.4.3 Wall R-Value Calculations

Solid Concrete and Masonry Block Basement Walls

Table A.25 shows the R-values used for uninsulated solid concrete and masonry block walls. The
uninsulated wall R-value assigned to these three wall types is the same as is used for above-grade mass
walls. Refer to Section A.2.3 for the derivation of these values.

Table A.25. Basement Wall Types and R-Values

Mass Wall Type Uninsulated Wall R-Value

Solid Concrete or Masonry R-1.6
Masonry Block with Empty Cells R-1.8
Masonry Block with Integral Insulation R-2.4

The insulated wall R-value is

Basement Wall Rval = Re ff + Rwall + Rcont (A.16)

where Reff = the effective R-value of an interior furring and insulation system as determined by the
rated R-value of the cavity insulation (see Table A.15).
Rwall = the R-value of the uninsulated wall (see Table A.25).
Rcont = the rated R-value of the continuous insulation.

Wood-Frame Basement Walls

Wood-frame basement wall R-values are established similarly to above-grade wood-frame walls
(see Section A.2.1). Due to differences in the code-referenced ASHRAE standards, the 1992 and 1993
MEC (CABO 1992, 1993) framing factors are different from the framing factors used by the 1995 MEC
(CABO 1995) and the 1998 and 2000 IECC (ICC 1998, 2000).

Table A.26 gives the assumed heat flow paths for basement wood-frame walls. Equation A.17
gives the wall Uo for the 1992 and 1993 MEC, and Equation A.18 gives the wall Uo for the 1995 MEC
and 1998 and 2000 IECC. In both cases, 2x6 16-in. O.C. construction is assumed. A wall R-value is
obtained by inverting the results of these equations.

A.25
 Table A.26. Heat Flow Paths for Wood-Frame Basement Walls

Description R-Value at Studs R-Value at Insulation

Outside Air Film 0.25 0.25
Plywood 0.77 0.77
Continuous Insulation Rcont Rcont
Wood Studs 6.88 --
Cavity Insulation -- Rcavity
1/2-in. Gypboard 0.45 0.45
Inside Air Film 0.68 0.68
Total Path R-Value 9.03 + Rcont 2.15 + Rcont + Rcavity

For the 1992 and 1993 MEC:

 0.15 0.85 
Basement Wall U o =  +  (A.17)
 9.03 + Rcont 2.15 + Rcavity + Rcont 

For the 1995 MEC and 1998 and 2000 IECC:

 0.25 0.75 
Basement Wall U o =  +  (A.18)
 9.03 + Rcont 2.15 + Rcavity + Rcont 

Insulated Concrete Forms

For ICF walls, the depth of insulation is assumed to be the same as the wall height. Below-grade
ICF wall R-values are calculated as:

ICF R -value = 0.68 + Rm × 0.89 (A.19)

where Rm = the manufacturer’s reported R-value, as entered by the user. (Refer to Section A.2.6 for
additional information on ICFs.)

Other Basement Walls

For Other wall types, the depth of insulation is assumed to be the same as the wall height. The
user must enter and be prepared to justify an assembly U-factor. The wall R-value is

1
Other Wall R -value = (A.20)
Assembly U-factor

A.26
A.4.4 Required Basement Uo in Locations Without Requirements

Basement wall requirements in the MEC and IECC do not apply to locations with HDD <1500.
In MECcheck, however, the user may receive credit for insulating basement walls in these locations. In
this case, the requirement is assumed to be an uninsulated wall of the type selected by the user, with some
exceptions.

A.5 Crawl Space Walls

The methodology for calculating heat loss through crawl space walls is identical to that described
above for basement walls.

The crawl space wall calculation requires the same inputs as the basement wall calculation. In
computing the code building UA, these same inputs are used except for the insulation R-value. For the
code building, the required UA is derived from Equation (A.15), except that the MEC Uo used in this
equation comes from the crawl space wall requirement rather than the basement wall requirement.

For crawl space walls having an inside ground surface 12 in. or more below the outside finished
ground surface, the code only requires the insulation to extend 12 in. below the outside grade. In this
case, the code building in the UA comparison is assumed to be fully insulated above outside grade and
insulated to 12 in. below outside grade.

For crawl space walls having an inside ground surface less than 12 in. below outside grade, the
code requires the insulation extend downward vertically and inward horizontally a total distance of 24 in.
from the outside grade surface. In this case, it is necessary to account for the horizontal insulation
required by the code in the MECcheck software (DOE 1995c). The 1989 ASHRAE Handbook:
Fundamentals does not provide an estimate of the effect of horizontal insulation on the heat loss through
the crawl space floor (ASHRAE 1989). Therefore, the horizontal insulation is accounted for in the UA
calculation by assuming both the insulation and the wall extend down vertically 24 in. below the outside
grade. In the UA calculation, this assumption increases the area of the crawl space wall beyond the actual
vertical wall area. This vertical insulation assumption, when the insulation is actually horizontal, is
reasonable because the length of the heat flow path through the soil to bypass the insulation is about the
same in either case. The same assumption is made for both the code building and the proposed building.

A.6 Slab-On-Grade Floors

To calculate foundation heat losses, heat loss values for slabs were taken from Huang et al.
(1988).(a) In this methodology, the heat loss unit for below-grade foundations is in terms of linear feet of
perimeter (F-factor) instead of square feet of surface area (Uo-factor). A Uo-factor is multiplied by a
surface area and degree-days to obtain the total heat loss. An F-factor is multiplied by a perimeter length
and degree-days to obtain the total heat loss. These F-factors are shown in Table A.27. The F-factors are
given in the referenced paper for insulation both on the exterior and interior of the foundation wall. The

(a) Sufficient data were not available from this source to model heat losses from common basement and
crawl space insulation configurations, so this source was used only for slab-on-grade foundations.

A.27
F-factors vary only slightly by insulation placement, so the average of the exterior and interior insulation
placement was used. The same F-factors were used for heated and unheated slabs. Huang et al. (1988)
did not present F-factors for insulation levels above R-10 for slab insulation 2-ft deep; therefore, F-factors
were considered to be constant for insulation levels above R-10 for this configuration. Additionally,
F-factors were considered to be constant for all insulation levels above R-20, regardless of insulation
depth. This assumption was deemed reasonable because little is gained by the additional insulation
(above R-20, most of the heat loss occurs under and around the insulation).

Table A.27. Slab-On-Grade Floor F-Factors

Insulation R-Value 2-ft Insulation Depth 4-ft Insulation Depth

R-0 1.043 1.041
R-5 0.804 0.744
R-10 0.767 0.684
R-15 0.767 0.654
R-20 and Above 0.767 0.636

In the MECcheck software, slab perimeters can be insulated to any depth up to 4 ft (DOE 1995c).
To calculate heat loss for any combination of insulation depth and R-value, quadratic curves were fit
through the data in Table A.27. The resulting quadratic Equation (A.21) gives the F-factor as a function
of insulation depth. The applicable coefficients for Equation (A.21) are given in Table A.28 and are
determined by the insulation R-value. R-values range from R-0 to R-20.

F-factor = intercept + coef 1 x depth + coef 2 x depth2 (A.21)

where depth = the distance the insulation extends downward (or downward and outward) in feet.

A.28
 Table A.28. Coefficients for Slab F-Factor Equation (A.21)

R-Value intercept coef 1 coef 2

R-0 1.042 0.0013 -0.0004
R-1 1.042 -0.0967 0.0144
R-2 1.042 -0.1293 0.0188
R-3 1.042 -0.1459 0.0207
R-4 1.042 -0.1562 0.0217
R-5 1.042 -0.1635 0.0223
R-6 1.042 -0.1692 0.0227
R-7 1.042 -0.1739 0.0230
R-8 1.042 -0.1781 0.0233
R-9 1.042 -0.1819 0.0236
R-10 1.042 -0.1855 0.0240
R-11 1.042 -0.1836 0.0231
R-12 1.042 -0.1819 0.0222
R-13 1.042 -0.1805 0.0215
R-14 1.042 -0.1792 0.0208
R-15 1.042 -0.1780 0.0203
R-16 1.042 -0.1770 0.0197
R-17 1.042 -0.1760 0.0193
R-18 1.042 -0.1751 0.0188
R-19 1.042 -0.1743 0.0184
R-20 1.042 -0.1735 0.0180

A.7 References
American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (ASHRAE). 1985.
1985 ASHRAE Handbook: Fundamentals. Atlanta, Georgia.

American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (ASHRAE). 1989.
1989 ASHRAE Handbook: Fundamentals. Atlanta, Georgia.

American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (ASHRAE). 1993.
1993 ASHRAE Handbook: Fundamentals. Atlanta, Georgia.

American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (ASHRAE) 1996.
BSR/ASHRAE/IESNA Standard 90.1-1989R, “Energy Code for Buildings Except Low-Rise Residential
Building.” First Public Review Draft, March 1996, Atlanta, Georgia.

A.29
American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. ASHRAE Transactions
V. 104, Pt.2 (TO-98-25-4), Table 5 Atlanta, Georgia.

Anderson, R. G., and D. B. McKeever. 1991. Wood Used in New Residential Construction in the United
States. American Plywood Association; American Wood Council; National Forest Products Association;
Southern Forest Products Association; Western Wood Products Association; and the Forest Service, U.S.
Department of Agriculture, Washington, D.C.

Building Foundation Design Handbook, K. Labs, J. Carmody, and R. Sterling, Underground Space
Center, University of Minnesota, 1988.

Council of American Building Officials (CABO). 1992. Model Energy Code; 1992 Edition. Falls
Church, Virginia.

Council of American Building Officials (CABO). 1993. Model Energy Code; 1993 Edition. Falls
Church, Virginia.

Council of American Building Officials (CABO). 1995. Model Energy Code; 1995 Edition. Falls
Church, Virginia.

DeCristoforo, R. J. 1987. Housebuilding--A Do-It-Yourself Guide. Sterling Publishing Co., Inc., New
York.

Aspen Publishers, Inc. Energy Design Update. March 1993. New York, New York.

http://www.buildinggreen.com/products/aaconcrete.html (Environmental Building News - Volume 5

Number 2, March/April 96 - hebel block)

Huang, Y. J., L. S. Shen, J. C. Bull, and L. F. Goldberg. 1988. “Whole-House Simulation of Foundation
Heat Flows Using the DOE-2.1C Program.” In ASHRAE Annual Meeting (Technical Papers), vol. 94,
part 2, pp. 936-958, CONF-880627. June 25-29, 1988, Ottawa, Canada.

International Code Council (ICC). 1998. International Energy Conservation Code; 1998. Falls Church,
Virginia.

International Code Council (ICC). 2000. International Energy Conservation Code; 2000. Falls Church,
Virginia.

Kosny, J and J. E. Christian. 1995. Steady-State Thermal Performance of Concrete Masonry Unit Walls
Systems; Thermal Performance of the Exterior Envelope of Buildings VI. Oak Ridge National Laboratory,
Oak Ridge, Tennessee.

Oak Ridge National Laboratory (ORNL). August 2001. Whole-Wall Thermal Performance Calculator.
Available URL: http://www.ornl.gov.

A.30
U.S. Department of Energy, 1995. Housing Characteristics1993-Residential Energy Consumption
Survey. DOE/EIA-0314(93). Washington, DC.

U.S. Department of Energy (DOE). 1995a. 1993 MECcheckTM Manual, 1993 Model Energy Code
Compliance Guide, Version 2.0. PNL-11087, Washington, D.C.

U.S. Department of Energy (DOE). 1995b. 1993 MECcheckTM Prescriptive Packages, 1993 Model
Energy Code, Version 2.0. PNL-11087, Washington, D.C.

U.S. Department of Energy (DOE). 1995c. 1993 MECcheckTM Software User’s Guide, 1993 Model
Energy Code, Version 2.0. PNL-11087, Washington, D.C.

A.31
 Appendix B

Prescriptive Packages Prototype House Sensitivity Analysis

 Appendix B

Prescriptive Packages Prototype House Sensitivity Analysis

Although the prescriptive packages apply to all residential dwellings except high-rise multifamily
buildings, the analysis used to create the packages was performed using only two building prototypes (see
Section 5.2.3) combined with four different foundation insulation configurations. To establish the
prescriptive packages, specific envelope component areas had to be assumed for the prototypes. If the
relative areas of each envelope component vary significantly from those assumed for the prototypes, the
prescriptive packages lose some accuracy in matching (i.e., meeting or slightly exceeding) the Model
Energy Code (MEC) envelope requirements. For example, a prescriptive package having relatively low
wall R-value requirements and relatively high R-value requirements for other components may not
comply with the MEC for a house with a very high amount of wall area. To quantify the impact of
applying the prescriptive packages to different house types, we conducted a sensitivity analysis using five
different single-family houses with the envelope dimensions given in Table B.1. Section B.1 documents
the results of the sensitivity analysis. All analyses were based on 1992 MEC requirements (CABO 1992).

A secondary aspect of this sensitivity analysis was an assessment of the relative accuracy of two
different methods for treating window area in the prescriptive packages: 1) treating the window area as a
percentage of the gross exterior wall area and 2) treating the window area as a percentage of the
conditioned floor area. The accuracy of these two methods is discussed in Section B.2.

B.1
 Table B.1. Prototype Houses Used in Sensitivity Analysis

Split Level House (baseline used to create the prescriptive packages)

Gross Wall Area 1736 ft2
Ceiling Area 1418 ft2
Floor Area 1418 ft2
Perimeter 155 ft2
Door Area 56 ft2
Conditioned Floor Area 1890 ft2
Window Area (% of wall area) 15%
Moderate-Size Ranch House
Gross Wall Area 1488 ft2
Ceiling Area 1890 ft2
Floor Area 1890 ft2
Perimeter 186 ft2
Door Area 56 ft2
Conditioned Floor Area 1890 ft2
Window Area (% of wall area) 15%
Moderate-Size Two-Story House
Gross Wall Area 1984 ft2
Ceiling Area 945 ft2
Floor Area 945 ft2
Perimeter 124 ft2
Door Area 56 ft2
Conditioned Floor Area 1890 ft2
Window Area (% of wall area) 15%
Small Ranch House
Gross Wall Area 1072 ft2
Ceiling Area 990 ft2
Floor Area 990 ft2
Perimeter 134 ft2
Door Area 36 ft2
Conditioned Floor Area 990 ft2
Window Area (% of wall area) 12%
Large Two-Story House
Gross Wall Area 3360 ft2
Ceiling Area 2700 ft2
Floor Area 2700 ft2
Perimeter 210 ft2
Door Area 56 ft2
Conditioned Floor Area 5400 ft2
Window Area (% of wall area) 18%

B.2
B.1 Sensitivity to House Dimensions
The intent in developing the prescriptive packages was that a home meeting the requirements of
any of the prescriptive packages would meet the MEC envelope requirements; i.e., the whole-building UA
of the resulting home should be equal to or slightly below the whole-building UA of the same home built
to comply exactly with each of the MEC envelope component requirements. This analysis attempts to
answer the question, “How accurate are the prescriptive packages in terms of meeting or slightly
exceeding the MEC requirements when applied to common house designs with different dimensions?”

B.1.1 Methodology

To determine the impact of applying the prescriptive packages to alternative house types, the
difference given by Equation (B.1) was computed for the prescriptive packages developed for all climate
zones in the continental United States (Zones 1-17).(a)

MEC UA − Package UA
Percent Difference = × 100 (B.1)
MEC UA

where MEC UA = the maximum whole-building UA allowed by the MEC for the house type
under consideration.
Package UA = the whole-building UA of the house type under consideration when built to the
specifications of a given prescriptive package.

The prescriptive packages were applied to each of the five basic home types shown in Table B.1
using three different foundation types, for a total of 15 house configurations. At the time of this
sensitivity analysis, a total of 374 prescriptive packages were proposed for 17 zones across the country.(b)
Of these, 358 prescriptive packages were used in the analysis.(c) For each house configuration, Equation
(B.1) was computed for each of the 358 packages and each of the following three foundations types:

1) a crawl space with floor insulation

2) a basement with insulated walls
3) a slab-on-grade foundation.

(a) Packages for Zones 18 and 19, which apply only to Alaska, had not yet been developed at the time
this analysis was done.

(b) This analysis was based on the Version 1.0 Prescriptive Packages developed for the 1992 MEC.

(c) Sixteen packages were removed from the sensitivity analysis because they exceeded the MEC
requirements by a large margin and therefore had a large effect on the average differences. For
example, in Zones 1 and 2, several packages were offered with no floor insulation requirement (R-
0). These packages tend to comply by a large margin if the foundation is a basement or slab-on-
grade, even though these foundation types have no insulation.

B.3
 Note that Equation (B.1) can give both positive and negative differences. A negative difference
indicates that the house built to the MEC requirements has a lower UA than the house built to the levels
specified by the prescriptive package under question. Therefore, a negative difference indicates that the
prescriptive package does not comply with the thermal envelope requirements of the MEC for the
particular house type. A positive difference indicates that the prescriptive package exceeds the MEC
thermal envelope requirements.

Two types of averages across all the climate zones and prescriptive packages were generated:

1) Table B.2 shows average absolute percent differences that were generated by Equation (B.2).
To derive these averages, the absolute value of the individual differences for each package
were summed and then divided by the number of packages.

358 MEC UA − Package UA[i]

∑
i=1 MEC UA
Average Absolute % Diff. = × 100 (B.2)
358

2) Table B.3 shows the average difference without using absolute values. Table B.3 indicates
whether the packages, on average, exceed or fall short the MEC UA requirements. A positive
number indicates the MEC requirements are exceeded on average. A negative number
indicates the MEC requirements are not met on average. Equation (B.3) was used to
calculate the overall average percent differences shown in Table B.3. To derive these
averages, the individual differences for each prescriptive package were summed and then
divided by the number of prescriptive packages (358).

358 MEC UA − Package UA[i] 

∑  
i=1 MEC UA 
Average Absolute % Diff. = × 100 (B.3)
358

Table B.2. Average Absolute Value of Percent Difference

Percent Error
Home Type Floors Basement Slabs
Split Level 1.4 1.7 1.1
Moderate Ranch House 1.8 1.6 1.5
Moderate Two-Story House 2.8 2.5 2.3
Small Ranch House 1.2 1.8 1.3
Large Two-Story House 4.1 3.6 3.2

B.4
 Table B.3. Average Percent Difference

Percent Error
Home Type Floors Basement Slabs
Split Level 1.3 1.6 0.6
Moderate Ranch House 0.4 0.9 -0.4
Moderate Two-Story House 2.2 2.3 1.7
Small Ranch House 1.1 1.6 0.5
Large Two-Story House 4.1 3.6 3.1

B.1.2 Interpreting the Results

Table B.2 indicates the average differences of the absolute values of the percentage differences
between prescriptive package requirements and the MEC requirements are reasonably small, with a
maximum difference of 4.1% and a difference of less than 2% for most house/foundation configurations.
The percentage differences were not large enough to warrant additional sets of prescriptive packages for
different prototypes.

A positive difference in Table B.3 indicates that on the average the prescriptive packages exceed
the MEC requirements. A negative difference indicates that on the average the prescriptive packages do
not meet the MEC requirements for the given house configuration. The values in Table B.3 indicate that
only one house configuration (the moderately-sized ranch house with a slab foundation) produced a very
small negative average of -0.4%. The maximum average percent difference across all house types
examined was 4.1% in the direction of exceeding the MEC requirements.

Table B.3 indicates that the prescriptive packages are conservative in the sense that they generally
result in homes that slightly exceed the MEC requirements. The differences for the split-level house
should be very close to zero because the prescriptive packages were based on that prototype. The average
difference is 1.3% for floor foundations, 1.6% for basement foundations, and 0.6% for slab foundations.
The reason these packages exceed the MEC requirements is that only commonly available R-values were
used in the analysis, making it virtually impossible to exactly meet but not exceed the MEC requirements.
For example, although a package might comply with R-17 floor insulation, the requirement was listed as
R-19 because R-19 was the closest complying floor insulation level that was used in the analysis.

B.2 Sensitivity to Window Area Calculation

The total heat loss rate (the UA) of any residential building is greatly affected by the window area
for two reasons. First, windows normally have much greater heat loss rates (i.e., much lower R-values)
than the other major envelope components (opaque walls, ceilings, and foundations). Second, window
area can vary greatly from house to house; low-end houses tend to have a small amount of window area
while luxury houses can have a huge amount of window area. The window area must be accounted for in
the prescriptive packages─simply presenting a window U-factor requirement without a window area
limitation will not allow compliance with the MEC to be determined.

B.5
 The window area cannot be represented in square feet (e.g., 100 ft2, 150 ft2, etc.) in the
prescriptive packages because this representation does not account for the window area relative to the
area of the other components. We considered two different methods for addressing the window area:

1. window area as a percentage of conditioned floor area

2. window area as a percentage of gross wall area.

Presenting the prescriptive packages as a percentage of the conditioned floor area is simpler for
the builder because the conditioned floor area is usually simpler to calculate than the exterior wall area
and is normally a known quantity. However, reviewers responded overwhelmingly in favor of computing
the window area as a percentage of gross wall area. To help formulate a decision on this issue, we
reviewed the impact the two calculation methods had on achieving compliance across all climates zones
for the various single-family house types and foundation types. We determined that representing the
window area as a percentage of wall area is more accurate in matching (meeting or slightly exceeding) the
MEC requirements.

The MEC requirements are a function of the wall area, the ceiling area, and the foundation area.
The problem with representing the window area as a percentage of the conditioned floor area is that the
conditioned floor area is not an equal proportion of the total envelope area for different house types. The
conditioned floor area of the split-level house is 41% of the total envelope area, but the conditioned floor
area of the large two-story house is much higher─62% of the total envelope area. The prescriptive
packages were generated for the split-level house. If the window area is represented by a percentage of
the conditioned floor area, the 358 packages fail to comply with the MEC by an average of 14.8% for the
large two-story house with a window area of 18% of the conditioned floor area. This matching of the
MEC requirements is much poorer than the 4.1% difference for the two-story house with the windows
area represented as a percentage (18%) of wall area (see Table B.2). The window area as a percentage of
conditioned floor area approach is also less accurate for the other single-family house prototypes.
Window area is represented as a percentage of wall area in the prescriptive packages primarily because of
the greater accuracy in matching the MEC requirements.

B.3 References
Council of American Building Officials (CABO). 1992. Model Energy Code; 1992 Edition. Falls
Church, Virginia.

B.6